Would it be rude to give my girlfriend pointers on how to cook better?
Not if you do it kindly, have you thought about teaching her instead?
Cooking is an art, everyone has to learn on his own.
While everyone has their own style, it is okay to give somebody tips on how they can do something different. It will help her to know different ways to make something.
I don't have time to fully teach her, but I am willing to at least give pointers.
It's understandable that you're busy! As long as the pointers you give her are thoughtful and kind, not rude or judgmental, I'm sure she'll take them to heart. You two can also consider watching a cooking show together for ideas!