>>1264164I have the feeling you're putting too much pressure on making it "feel like a date."
Nobody likes that kind of pressure and you won't either. Focus on having fun. Women love fun guys who have passion for what they do. Taking her hiking, which I assume is something you have passion for, is a great opportunity for her to see what kind of person you are.
As for asking her, just bring it up casually that you are going hiking at [insert date and time here] and she's welcome to come along if she's interested. If she is, exchange numbers (if you haven't already) and work out the details later.
If she says she is busy, don't bargain or try to reschedule, just say "another time then" or a variation. Try again on another day. If she is interested in you she will make the time to hang out.