The typical swim team swim suit looks like this. This is the Speedo Aquablade from Swimoutlet.com. It has no bra cups and the only lining is a small patch on the crotch.
This is the Sporti Solid Y-Back Workout Bikini Top from Swimoutlet.com. This can easily be worn under the swimsuit. It has a racer back so the straps will not show and comes in a variety of colors to match your racing suit. It should not give additional drag in the water.
To give even more modesty to your suit you can add a bra cup into the bikini top. Simply make a snip in the lining of the top at both sides. Make sure to only cut the lining (this is the inside layer). Then you can insert a molded bra cup into each slit.
These molded bra cups are everywhere. They are in many of your other swimsuits or sports bras you already have. Look for the slits and pull them out.
Now your swimmer can swim with confidence!
UPDATE: Find other cup options at: Modesty: The Sports Bra
For other alterations read: