I started out with a regular underwire bra, but it wasn't very comfortable when moving around and doing all the activity that happens on the ice, so for me, a sports bra is necessary. Right now I wear an athletic top with a built-in sports bra. I'm not sure what I'll do when I start competing or performing. Any kind of built-in bra would have to go all the way around. If I just sewed bra cups into the front of a skating dress, I don't think it would do much supporting.
For those who want to wear regular bras, they do make these little clips which draw the straps together at the back. It works for under sporty styles or X-backs, where regular bra straps would normally show. I bought a package of four clips for $1. Haven't had the opportunity to use them, yet, but they look like they'll do the trick.