One good solution is to find a suit that has a second layer of fabric over the chest area. It's best if the outer fabric layer has a design feature that adds some fullness, so the top layer of fabric isn't stretched tight across the girl's chest. It's even better if the design feature is appropriately fashionable.

Another possibility is to wear an outside layer, such as a shrug, bolero, or even a tankini top, over your regular suit. Again, it's best if the outside layer has a bit of fullness and is appropriately trendy or fashionable. Scout your local stores so you're aware of what's in style.

For examples of suits which ModestSwimm.com custom-designed and sewed especially for preteen girls, check out the  swimsuit photo gallery below.

Preteen Swimsuit Gallery

All of the following suits feature a second layer of fabric over the bodice area.
(Suits are shown on hangers, then on models.)