We are conditioned by our mothers and social pressures to wear a bra from puberty onwards and, mostly, never question the "need" for this. Sadly, I was well into my late 60s when I realised that shoving myself into these horrible, uncomfortable and ridiculous garments was not a requirement and the world would not end if I Just Said No.
Oh, happy day! How I wish I'd been brave enough to do it sooner. As GSM says, there are bralettes and crop-tops if you do feel the need of a little support or don't want your nipples on view through a tee shirt. And, if you don't want to feel the bounce while you're jogging etc, take a look at the hundreds of sports bras on offer.