Illy,
I think it is the hormones in birth control that cause breast growth. And, unfortunately, I don't think there are any out there that don't contain hormones.
For those wondering, birth control pills trick your body into thinking it is pregnant by regulating the levels of progesterone, and sometimes estrogen. If your body thinks it is pregnant, it doesn't release an egg. Some people may be sensitive to the progesterone, and hence encounter breast growth.
If you are afraid of becoming bigger, look into the condom alternatives. I recommend lambskin, personally. They just feel better all around. My wife and I tried the polyurethane condoms for people sensitive to latex and I felt like I had one of those gloves you wear when you color your hair on my willy!
Punchy