We have a skin infection going around in our house right now, and the vet's instructions were to bathe the cats with a special shampoo. Once we get them lathered up, the shampoo has to sit on their skin for 10 minutes before rinising off!
What's the best way to bathe a cat without injury to either cat/human, and the least amount of stress on the cat?
A cat will fear drowning far more than being wet.
Having feet on the ground should make it a lot calmer about the process.
One method I've used for flea medication baths is the kitty burrito - wrap the cat securely in a towel then immerse cat and towel in the water (keep the water warm without being hot). This works best if the water isn't deep - you want enough for the medicated shampoo to soak through the towel to the cat's skin then use the towel to rub the shampoo in once the towel is soaked. Talk to the cat the whole time: very few cats like being bathed. The combination of your voice and a firm grip will help.
For your situation, I'd use two tubs - the shampoo tub and a rinse tub. The shampoo tub can be a bucket inside a larger tub that you use to rinse off (like sitting in your shower).
To rinse off, remove the cat from the shampoo tub (preferably with an accomplice to get it out of the way - otherwise have both prepared in advance) and stand it in the rinse tub, then pour clean warm water over the towel. If you've got an accomplice, have them remove the towel while pouring (yes, I've done this while giving a cat a flea bath).
Use a clean, dry towel to dry the cat off as much as possible, and have a heater somewhere the cat likes so it can finish drying somewhere warm.
Unless you've got an unusually tolerant cat, you'll probably get snubbed for a while: have some of the cat's favorite treats on hand to give out after the bath so the cat has something nice to associate with it.
It does depend a lot on the cat - I've seen a very elderly cat object loudly to going into the tub then relax and start purring and rubbing her head against me once she was in the water (she had arthritis - I suspect the warm water felt good on her joints. She always had a radiant heat heater set out to finish drying), and a young male who had to be actively discouraged from jumping in to share the shower with me, as well as the more typical reactions of "oh, no, I'm not doing that".
Since we're having to give the cats multiple baths (every 2-3 days), I'm trimming their claws on the "off" bath days to give them time to dull a bit (a recently trimmed claw can still be sharp-ish).
I have a handheld shower head installed in my bathtub, so I just climb into the bathtub with the cat (fully clothed). I found it's easier to manuever everything when I'm on the same level as the cat and not leaning over the bathtub wall. The handheld shower head makes it easy to direct the water where I need it.
Two of the cats are easy to bathe, they just cry and stand there pitifully. The other two fight and claw to get away. When I'm bathing the fighters, I'll either hold them by their scruff (not because they go still, they don't; it's a place where I can grab a lot of skin to hold them securely), or wrap my hand around their chest/shoulders (usually just while I'm working on the scruff, as the scruff is much more secure).
Fortunately, my husband helps with the drying part. We use two towels to wrap them up and rub them down a bunch. Normally if there's a chill in the house I'll also blow dry them a bit (but with the current medicated shampoo I'm not allowed to do that, so we let the house get a bit warmer than usual after bathing).
