So, what is the normal time frame for a young girl to start developing breasts? It varies, but for the most part it's tied to puberty — when she begins, or is soon to start, menstruating.
Time was, we used to say "around age 12," but that guideline is long since outdated. Many young girls are starting menstruation (menses) at age 9, and with it can come the development of breast buds that are prominent enough to warrant a bra — and one that's roomier than the old-fashioned "training bra," which, frankly, was never designed to train your breasts to do anything. It was designed to help girls get used to wearing elastic around their bodices, along with shoulder straps. Today, children 10 and 11 are ofttimes already wearing some type of upper support garment. Why is this?
There are several schools of thought. One is that we are healthier today than, say, a century ago (when girls didn't start menstruating or having breast development until after ages 14–16). Another is that kids are carrying more weight now, and stored within that body fat is an extra supply of estrogen, which can jump-start puberty (and potentially increase the risk of breast cancer in the future).
We are also consuming foods that contain estrogen — another potential cause of early sexual maturation. Keep in mind, as well, that obese children (including boys) can also appear to be developing breasts when in fact the tissue is made up only of fat, without any ducts and lobules. A young girl in this situation may need to wear a bra, so as not to feel additionally embarrassed — it doesn't matter what that extra flesh up there really is.
Most mothers, though, can anticipate their daughters starting to shop for bras at around age 11. It would be great to actually be able to teach her what a properly fitting bra should look like, but peer pressure will override your recommendations. Victoria's Secret® commercials will have gotten to her first, insisting that she get a bra that is too small for her size. Expect it.
The development of breast buds with the attendant bra shopping is, however, still an opportune time to discuss sex and hygiene and other mother/daughter issues — be sure to take advantage of this milestone she is reaching.