I see nothing wrong with it - it sounds like fun, as a matter of fact.
I once read a memoir called "A Friend Like Henry" about a little boy on the autism spectrum whose golden retriever dog (named "Henry" after the Thomas the Tank Engine character) was like a therapy animal and helped him overcome many challenges, and the mother talks about making bath time more fun for her son by allowing Henry in the tub with him - otherwise, the boy would have needed to have all his Thomas trains lined up around the tub to watch him. Kind of like how I used to place my Beanie Babies all around the bathroom while I was having a bath as a kid. xD Anyway, the mother wrote that having the boy and dog bathe together was well worth it, even though the bathroom ended up being a royal mess afterwards.
I don't think I'd be able to interest my mom's dog in a bath with me, though - she just got groomed, and she doesn't like baths normally.
.....This isn't about dogs necessarily, but I also loved the part in the movie "Fly Away Home" where the young girl has a shower with all the little goslings. It was super cute. 
_________________
I wish Sterling Holloway narrated my life.
"IT'S NOT FAIR!" "Life isn't fair, Calvin." "I know, but why isn't it ever unfair in MY favor?" ~ from Calvin and Hobbes