Yves, you gave no details on your communication with this girl after the night of the party, nor did you mention the basis for your feeling she might have buyer's remorse. At any rate, yes, you should ask her out.
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How do I invite her without sounding like I'm playing her?
ASKING A GIRL OUT ON A DATE DOES NOT MAKE IT SOUND LIKE YOU'RE 'PLAYING HER'! The whole idea is to ask a girl out. Get that straight. Put yourself in the same physical space with her, have a blast, work whatever game you now possess, and then taste her sweet pussy.
Try to plan your meeting with this girl around an activity more fun and interesting than coffee. Picking something or someplace fun shows her you're creative and not like every other guy out there. And it takes pressure away from the idea of labeling the get-together "a date," which in your case, if there's a chance she has buyer's remorse, will help you. (Oh, and don't bring up the make-out session the other night when asking her out; if she feels remorseful about it, you'll only be stirring up those feelings again, regardless of how you spin your line as a reversal.) At the very least, if you're gonna go for coffee, market the idea in a more dynamic way: "Hey, have you been to Lena's Bean downtown?...I hear they have the best chocolate jalapeño brownies anywhere!"
Good luck.