Find something cool like the country fair, rock concert, baseball game, nascar race, wine festival (whatever your thing is or any local cheesy event) and then chat up with her about whatever, then mention that you are going to this event and it would be cool if she could join you. If she says no, then tell her that she is missing out on a great time. Make it sound like you are going either way, so if she joins you or not, it's no big deal. Depending on what you are actually doing, you may or may not be going anyways. Pressure is off because you are inviting her to your fun time, not relying on her to be the fun time. If she says no, don't offer an alternative, wait for later. If she says yes, then there you go.
good luck, ask her, she probably wouldn't mind going out and having fun with you.