hmm....i don't know if b-ball with a female is the best date. Well if she likes to hoop then go for it. But I wouldn't ask her to play basketball. I say you guys meet up at at bowling alley, or the movies, or go to each other's house, or etc. BUT, remember it doesn't matter where you guys go or do as long as you have
FUN.
As for asking her. It's simple, just a simple "what are you doing this weekend" is good. If she's not doing anything then ask her out.
Example
You: hey, what are you doing this weekend?
Her: hmmm... nothing, why?
You: Cool, lets play b-ball this Friday
But Basketball isn't a good idea but hey who I'm I to say whats fun. If you like it, she likes it go for IT! Good Luck