Just b/c she doesn't smell doesn't mean she isn't dirty.
I understand you can't do anything without your parents permission. But if you use the proper shampoo/conditioner and not really hot water (which I know you wouldn't anyway -use too hot water- not accusing you of anything) she won't get dry skin. Especially if you use the oatmeal and baking shampoo or shampoo for dry skin.
But you have do what you have to do.
My sister has a lab/springer mix that she doesn't bathe near as often as I bathe Keegan, and so when you pet him the hair FLIES.
Keegan b/c I keep her brushed and bathed isn't like that. When I leave their house, I just want to take a bath b/c I have dirty dog hair allllllllllllll over me. And of course Scooby loves his Aunt Stac soooo he tries to be in my lap all the time.