There's no reason a cheerleader ever has to run around in just a sports bra outside the gym.
I honestly don't see why wearing even just a t-shirt over it is such an issue. Even if it's "so hot!" outside, a tshirt should be cool enough to function in. Yes, for seniors, too. It's respectful to your community, even though I know most of you aren't trying to look sexual in a sports bra.