Is 34 b a good bra size for a teenager?

There's no one size that is "best" for a teenager. 34B is a healthy, average size however.

When you get into the Ds and DDs, especially with a smaller band size but with all sizes, a LOT of back problems begin to arise.

34 is not the measurement around the band, but actually the measurement from the back of the clasp around and over the top of the breast across the sternum. The cup size is the measurement across the nipple line and around the body, subtracted from the band size and numerically assigned to letters. (1=A, 2=B, 3=C, etc)