I'm a 34 DD and I end up just opting for the "eff it" and wearing a bra strategy. You will sometimes find me with my jersey zipped down past my boobs on a hot day where I am sweating a lot. I just don't care. And if anyone does, they've never voiced any appearances. Yeah, I have boobs. I'm a lady. It happens.

I do understand why that may not work for you, though. I second the ask them if they could buy you something else strategy. I love LG jerseys because they are very breathable. Sugoi also makes some. Neither brand is very see-through. I can wear whatever, basically. But I'm already in spandex. My version of modesty is basically, "I'm sweating a lot and working hard, so if someone is offended by that, I will be gone in 30 seconds and they can get over it".