You should be fine. Yes, BB30 bottom brackets are designed to work best with BB30 cranks, but there are several really good work-arounds.

I suspect the adapters you have are the plastic spacers that reduce the bearing diameter from 30mm to 24mm and take up the spindle length. Most people have no issues with them.

If you are unhappy with that, your next step should be to consider a conversion bottom bracket. These bottom brackets press into the frame, replacing the BB30 bearings and fit your crankset.

If you are hell-bent on going with a BB30 crankset, then yes, the Rival will work. BUT, you may still be using spacers. Sram made many of its BB30 cranks with extra long spindles so they also work in BB386 and BBRight bottom brackets.