I don't think not washing hair is gross, I only wash my kids hair if they go swimming to get the chlorine out. But the cradle cap does sound like it needs to be dealt with, and she needs a daily bath to wash everywhere else. What I would do is make the bath as fun as possible for a while until she gets used to it. At least then she's getting washed and you can then try deal with the hair.

You could try:
Food colouring in the water.
Cut out craft foam shapes she can stick on the wall and make things (I have done blue water with white foam 'icebergs' and sea animals, or pink water and cut out flower shapes to decorate the wall, etc).
Bath paint, crayons.
Even use washable paint yourself and paint the bath and make a little world with figurines to play with and no water and let her play in it during the day and get used to the bath.
Glow sticks in the bath.
etc.

ETA- I just googled and there is a whole website called 'bathactivitiesforkids' with tons of ideas.