Would this be safe to ride in?

Yes that would be fine. whatever you are most comfortable in works best.

Depends on the horse, if it’s a easy going horse sure. But if that horse were to throw you; you might want long sleeves at least to protect your arms. Until my daughters were good riders I made them wear a shirt with long sleeves, jeans, and boots. One of them wore a tank top, shorts, and tennis shoes one time. She was thrown off and got tore up pretty bad (full gallop). After that she listened to the ol’ man.

Even a nice horse can get spooked and throw you. I knew a young lady who was thrown and landed on a rock head first; almost killed her. So do be careful.

And have fun!

yes

might have bouncy breast syndrome,make sure they don't come out at a trot