What is the right way to sponge bathe a female?

Make sure that she has a solid shower chair in place, slip proof shower mat, and grab bars in place so she feels more secure. And a hand held shower head will be helpful and make cleaning her a bit easier as well.
Then help her in and help her wash up. Yes, you may get a little wet, but it's only water, so you won't melt.
And if she's getting cleaned up real good in the shower, she may only have to take 2 per week. And then you can use the extra large body wipes and waterless shampoo and conditioner caps for the in-between.
Both of those can be ordered on Amazon or Walmart.com.

I am not going to directly answer the question but I do have a suggestion.
Have her husband contact a Hospice in the area and see if she would qualify for Hospice.
Hospice does NOT mean she will die in a few months.
What Hospice WILL do is provide a Nurse that will come at least 1 time a week to check on her and order any medications. (yes medications are prescribed when on Hospice)
Hospice will also have a CNA come out at least 2 times a week to give her a bath or shower, order supplies. "Diapers", gloves, ointments, barrier cream, under pads are all supplied.
Hospice will also provide all the equipment that is needed to care for her safely.
Medicare, Medicaid and other insurance will cover Hospice so all the items that I mentioned will be covered.

Now to directly answer your question.
You should do what is safest for you and her.
A bed bath might be the safest if she is not steady on her feet or if the shower is not a walk in. It gets risky if you have to step into a tub to shower.
There are no rinse soaps that can be used. Most of the no rinse soaps can also be used on the head. (It is easier if her hair is short)
If the shower is what you want to do a shower chair is ideal or a bench. If a bench is used it is safer if it has a back.
If the shower is a walk in shower there are shower wheelchairs that make showers easy.
A sturdy commode could also be used, removing the "bucket" will allow you to clean her very well.

A few other things that will come in handy.
Non slip mat.
Shower shoes if she is walking. These are usually also non slip so it is easier to walk on a wet floor.

Search YouTube for ways to shower someone safely.

Hospice supplied my MiL with waterless shampoo caps for her hair. Hospice even came in three times a week to shower her. They also supplied all the supplies she needed, which included the bars she needed in the shower, and for her patio door. This was a hospice in PA. Hospice in New Mexico didn't supply anything since we were well supplied and brought her supplies with us when we moved her to our home.

Only complaint I had was I was not given much direction, or instructions and learned most of what was needed online. Then we didn't get notified hospice was involved until she was on it for about 2 months, and was notified she was not expected to live more than a couple of weeks.

Youtube video available. Simply google "How to sponge bathe an adult".

we installed a bidet for my mom and when we put it in, we also put arm rails on the toilet. We got the bidet genie but there are others. It was a life safe for cleaning daily. No matter what, when mom toilets, the front and back are rinsing her and then drying her. The water is warm and the seat is warm. I talk to her the entire time so she doesn’t bolt! The caregivers told me it is wonderful because they didn’t trust it and found she was “clean as as whistle”. Lol. The showers are conducted in an overly heated bathroom and once she is under the shower she is okay. Then into a warm robe and under a cover. OR; if she isn’t too antsy, she is lotioned, dried, dressed and then under the cover with a warm compress on her eyes. We call it the Spa Treatment! When a bed bath was in order, the hair is done with a wash cloth. Her hair is short and this is done pretty easily. Just put a towel around her shoulders first.

I am caregiver for my Alzheimer's wife of 84 years old. She is wheel chair bound and I use a Hoyer lift to get her around. For bathing I place her on the toilet, strip her down (she makes no fuss) and give her a sponge bath then put on her clothes. Two times a day Upon waking and before bedtime her privates get get cared for. If she makes a mess she gets cleaned up right away. Putting her in the shower is to much a hassle.

Have her PCP order home care services for her; this will provide her ADL services and protect her safety as well as your safety and your well being. Get help !

Here is a cut and paste from my book "Dementia Care Companion" about the subject of bathing in bed:

Bathing in Bed
Bathing in bed may seem daunting at first, but with a little planning and the right equipment, it can be a relatively easy and smooth process.
·        Before attempting a bed bath, you’ll need to have mastered the procedure for changing bed sheets while the patient is lying in bed and unable to cooperate with you (described later in this chapter).
·        The following procedures are described in reference to a hospital bed. A hospital bed can make bathing in bed a lot easier by allowing you to adjust the height of the bed to a comfortable level so as to minimize strain on your back.
Preparing the Supplies
Prepare what you will need ahead of time so you won’t have to leave the patient alone during bathing. You’ll need:
·        Two buckets (one for soapy water, one for rinsing)
·        One waterproof sheet or a large towel to keep the bed dry
·        A few washcloths or sponges
·        A few bath towels
·        Soap, shampoo, and moisturizing lotion
·        Makeup items or shaving supplies
·        A set of clean clothes.
Safety First
·        Keep the room warm. Close the windows and turn up the heat as necessary. Keep the patient covered at all times. Uncover each area only when it is being washed.
·        Safeguard the patient’s privacy. Close the door and draw the curtains. Cover the patient with a towel before undressing them. Only undress the areas that are to be washed.
·        Have someone present to help you, especially if you have to roll the patient onto their side. Raise the bed’s guardrails to ensure the patient cannot fall out of bed.
·        Raise the bed to a comfortable height so you don’t strain your back.
·        Spread a waterproof sheet or a large towel under the patient so the bed does not get wet. Follow the procedure for changing bed sheets later in this chapter.
·        Use warm water for washing. Maintain a water temperature range of 100 to 110°F (38 to 43°C). The water should feel comfortably warm to your elbow.
Wash, Rinse, Dry, Inspect
·        Fill two buckets with warm water, one for soaping up a sponge or washcloth, and the other without soap for rinsing. Be prepared to change the water at least once during the course of bathing.
·        Wash with a wet washcloth and soapy water. Rinse using another washcloth and clear water. Dry the area before moving on to the next area.
·        To dry, spread a towel on the area, pat it, and remove the towel. Do not rub the towel on the patient’s skin, as it may cause the skin to break.
·        Wash a single area at a time. Uncover the area, wash, rinse, and dry, then cover it up again before moving on to the next area.
·        While washing, inspect the patient’s entire body for signs of skin rash, scratches, and red spots which can be a prelude to pressure ulcers.
Wash in Order
·        Start with the cleanest areas of the body, and progressively move on to areas that are less clean.
·        Wet a washcloth without soap. Gently wipe one eyelid from the inside and moving out, and then pat it dry. Repeat on the other eyelid, using a different part of the washcloth.
·        With soap and water, wash the face, ears, and neck. Rinse and dry before moving on.
·        Wash one side of the body, and then the other side. Wash the shoulder, arm, and hand, on both sides, then the chest and belly, including the belly button, then the hip, leg, and foot on one side, then the other. Wash one area at a time with soap and water, then rinse, dry, and cover before moving on to the next.
·        Pay special attention to areas with skin-on-skin contact or folds, such as the armpits, abdomen, belly button, and between the toes. These areas must be clean and dry to prevent skin irritation and fungi growth.
·        To wash the patient’s back, first roll the patient onto one side and wash one side of their back, and then roll them onto

lilstac: A bed bath can be accomplished with all items at the ready (small tub of warm soapy water, wash cloth and towel). Undress the elder in stages and then redress to prevent chills. Hair can be washed while not in a shower or bath tub.

In addition to checking YouTube for bed bath tutorials you might want to look at the other CNA skills videos - just search YouTube for CNA skills

ALWAYS WASH CLEANEST TO THE DIRTIEST.
Prepping is everything. Do bed change on bath day. Have laundry basket nearby. Clean sheets, pads and blanket.
-get two plastic basins. One for warm soapy water. Use favorite bath gel if her skin isn’t sensitive. One with clean warm rinse water.
-buy the cheap dozen package of washcloths from dollar store. They are thinner and easier to clean in crevices. Put 1/2 in soapy water and 1/2 in rinse water.
-get two fluffy large bath towels near you. Any creams, lotions, powder or barrier creams near you and OPEN them.
-as you roll, raise and turn her (whatever movements she tolerates) you will be removing dirty linens and replacing with clean as you go.
-completely disrobe her head to toe. Cover with sheet or blanket from the bed.
-start with face, eyes specifically. Rest of face then all around neck and shoulders. Rinse in same order. Toss washcloth in laundry basket.
-fold sheet down to expose arms. START WITH HANDS. (Think..you wouldn’t want to wash armpits then hands with same cloth. See?) work your way up arms, elbows, backs of arms to the armpits. Toss washcloth. Rinse with clean cloth.
-Wash chest and belly, then back to top of buttocks. Last wash under breast then under belly fold if there is one. Toss cloth. Rinse with clean cloth and toss. Cover with CLEAN FLUFFY towel.
-if needed change out dirty wash and rinse water for warm clean soapy and rinse water.
-uncover legs. Wash feet (if not bed bound the wash top of legs moving downward, front and back. Toss cloth. Rinse.
-Wash private area very well. Clean labia/vaginal area first. Get tenderly inside folds. Rise well. You can use the same cloth to clean her bottom and rectal area but never clean vaginal area with same cloth you have used on rectum. Same with bm clean up. Vagina first. Rinse well. Barrier cream on bottom and sacral patch if you use them. Cover with fluffy towel.

Now you gather laundry and do some clean up and finish bed changing, pillowcase change. Then make sure she if fully dry in all crevices. Bacteria and fungus love warm moist areas. Powder under folds. Lotion all over but elbows and heels especially. Dress her then both of you rest 💕
You will get the routine down quickly and modify as it best fits her needs and you.

For hair, suave makes a great dry shampoo. You spray it on, comb it and let it set a few minutes then brush normally. I’ve used this myself. It’s good to get a good shampooing occasionally but this really helps.

Good luck and God bless.