How should I pursue her without messing it up?

It sounds as though she likes you, as a friend at the very least. What I learned as a salesperson is that you don't get what you don't ask for. If you would like to date this girl, do the old-fashioned thing: call her up and ask her to dinner. Be a gentleman, and treat her with respect. If she says no, that's the worst that can happen. But if she says yes, then it's a good sign that she would like to find out more about you because she thinks you're interesting. Just because the two of you have different personality types doesn't mean a thing; most good marriages, in fact, are made of a husband and wife that have differing personalities. Conflicts are inevitable, but one person's strengths can help the other in an area of weakness, and vice versa.

take a chance, man. Call her up and ask her if you can take her to dinner. Use those exact words: "if you're interested, I'd like to take you to dinner. " I mean, what girl wouldn't like to be taken out by a man she's interested in?