You won't bulk up unless you really go for that by changing your diet and working out a LOT. If you just do some basic exercises (half push-ups where your knees are bent, or lift dumb-bells or bottles as someone else suggested) then you'll be fine.
Your muscles will get more toned, and better definition - you'll be able to see them better as the fat slims down, but you won't end up looking like a body builder
