I am leaving this summer to go to East Asia to lead and take part in a missions project. There is a girl I am quite interested in and she is going on the trip with us. The trick though is that I am moving to the country and staying for school rather than going back to the States.
I don’t want my feelings to get in the way or affect my ministry but I don’t want to just leave these thoughts and feelings bottled up for me to just “deal with it”.
LemonVibe 
Whoa now. Rein those horses in. You aren’t even dating yet and don’t know if she’s honestly compatible beyond friend. Be upfront with your situation if you decide to date and then go from there.
If you’re staying there and she’s going back, it doesn’t sound like there is a huge chance for a relationship to continue if anything were to develop.
I think you should:
1. Focus on your ministry first and foremost. Do the work that you’re being called to do.
2. Approach the situation without expectation. Be a good friend to this girl, and enjoy the summer that you share. If you go in with no expectations, you may be surprised by the outcome.