For sure, don't worry about bulking up! Ain't gonna happen
Strength training is far, far better than doing nothing, so if weights are what you like, by all means do weights! Besides, the extra muscle increases your metabolism and you'll have a better time at losing weight.
Cardio on campus was always hard for me, though we had a gym and all. All those little gym bunny girls really freaked me out and I could never go into the big cardio rooms without having an anxiety attack. I just felt so out of place. I did, however, find that aquafit was an awesome way to get cardio in on campus (for free) -- see if your school's pool has some classes. Even if there are people who I didn't want to see me exercise, my body was underwater
Besides, it was so much fun I stopped caring faster than I thought I would!