I managed to catch mice in a trap baited with little pieces of Kraft Singles. I frankly didn't have anything else suitable at the time, and I was surprised it worked.
However, I've heard of some traps that were pre-baited with artificial strawberry scent. Not sure if that's the best but maybe strawberry jam or different types of jelly or preserves.
Another thing is to be light on the amount of bait. If it's kind of thick it might be possible for the rodent to take a little piece off without putting enough pressure on the catch to trigger it. But if a mouse has to scrape hard that should trigger the trap.