being interested and refusing dates are mutually exclusive
if she likes you, she'll agree to go out with you
if she doesn't like you, she won't agree to go out with you
if she doesn't like you, and doesn't like/can't do the date, she'll just say I don't want to/I can't and be done with it
if she likes you but doesn't like/can't do the date, she might just go and not say anything, she might say no but then say yes if you alter the date a bit, she might reschedule, etc.
with all that in mind, don't say something like "will you go out with me", say something like "I haven't been to wendy's in sooooo long, I think I'm gonna go after school today, want to come?" or you can just alter 'want to come?' to 'come with me' or 'you should come with me'
you could also start by asking her opinion of the place/activity like "have you seen X-men:days of future past yet?", "I hear it's good", "want to go see it on Saturday?"
good luck, and try not to show your feelings if she says no, ask her out again later if she gives a legit reason, and realize that girls will never just say "i don't like you, f*** off" you'll have to realize that on your own after she turns down your 2nd/3rd/5th/7th date offer or if she gives an obviously BS/implausible excuse