If there were true feelings about each other, I'm sure you'd find a way to be more social (in a balanced way, not too social but not too much of a shut-in either) and she'd be more willing to do the things you like as well, like watching a movie at home, for instance, or having a meal at home, etc. Being extroverted doesn't necessarily mean you're constantly out on the town having fun, it just means you're confident enough to enjoy being around other people and preferring that over staying home, same way being introverted doesn't necessarily mean you have to be constantly stuck at home unwilling to have any sort of social interactions.
A lot of girls (even the more outgoing ones) do like a guy who's different from them in that aspect. Obviously this doesn't mean they often go for the shy, insecure and not confident type of guy (let's face it, being confident and master of your domain is attractive), but if you can work on those qualities, and tone down the emotional/sensitive to a point where it barely affects the equation, she'll be into that. She does tell you she misses you as it is, so just imagine how she'd feel if you mastered those qualities!