Even with the bath, maybe if you try turning on just the hot water it might get steamy in the bathroom. Dont put him in the bath, just sit in the bathroom with him that way the steam will clear him up a bit. I might just watch how hot it gets in there; dont want him getting overheated.
Also, if he gets really stuffy, try giving him two drips of nonmedicated saline drops in each nostril, wait about a minute, and then suck out his nose. You should do this before each bottle. Otherwise he might start sucking down too much air-which will give him a belly ache.
These are just a few tricks my pediatrician recommended. Colton got sick a few times when we lived with OH's mom because she smoked around him.. we moved out about two months ago and he hasn't been sick since
