Start a friendly conversation with her first, and then casually bring up the topic of prom into the conversation.
Engage her in the conversation, make her understand that prom would be really great if you could go with her. Ask her if should would be willing to go with you, let her know it would be a lot of fun to go to prom together.
Seek time with the girl and engage in a friendly conversation leading up to discussion of the prom. Say that you're looking forward to the event but that it would make it wonderful if you could be going with her. Ask, would she consider going with you?
I can't know whether you are in competition with several other hopefuls, but this approach will serve you far better than a casual, 'Let's go together' or 'How about it' which suggests that any old girl will do and you don't care much whether it's her or another girl. Good luck!