I bathe my dog in the bath tub and I am there with him and I keep the glass door closed so he wouldnt be able to jump out. I fill the tub like 1/4 of the way and I use a big plastic cup to wash him. ANd I think he feels more at ease that I am in there with him. Dunks is pretty good with the bath, its the cutting his hair & nails, cleaning his ears, and brushing him that he hates.

After his bath, I dry him off with a towel, then I put him down on the bathroom floor. There he would run around. I usually use a protable heater and set it on low and he would just sit in front of it. When I do use a blow dryer, he would run around thinking I was playing with him, but I just follow him with the blow dryer wherever he goes.
So you might want to try the portable heater thing... might work for your baby...