As for keeping baby clean, I'm not. I'm wiping her face and hands and checking there's nothing in the folds of her neck. Other than that she can stay sticky til her next bath. Otherwise it would be neverending. She doesn't get bathed every day because DH has to do it.
We didn't think about the fact there was just a shower here when we moved, so she has her bath in a baby tub on the floor of the shower. I can't manage the angle with my back issues so can get her in, and washed, but painfully, but the can't lift her safely up again as sometimes my back blocks when I am getting up. OK for me but not OK when carrying a baby. Damn horse.
DD1 is OK under the shower with one of us, but wet babies are slippery so I don't know how people shower with them. I have heard they do though.