A lot of people are making this too complicated. Assuming you're giving us the whole story, she almost certainly likes you - she's just shy. If you ask her out, she'll probably say yes. It might be awkward, because she'll still probably be shy, but I am six years older than you and I still have dates like that occasionally so you can't really do anything about it.
Don't pressure her. Don't say anything about relationships or you like her or does she like you or anything like that; it's just a way to force a confrontation that will only make her uncomfortable. Go out with her (which if she likes you she will), wait for a good moment, plant one on her lips, and she'll figure it out. If it works, great, if not, plenty of other ladies out there.