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".