I'm doing the quest Taking Care of Business. I started it, and got inside of Riften. I went to talk to all the people that owed debts, and for some reason I thought it would be funny if I just started hitting people. So I was being chased by many people, and I got away and quick traveled to somewhere else. I saved, and quit because I had something else to do. When I loaded my game, I went back to Riften to continue the quest. Keerava and Haelga both show up on my map, but Bersi Honey-Hand does not show up for some reason.. I've tried reloading my game and doing many things, but it still doesn't show. Is this just a horrible glitch.. Or is there something that's happening, such as another event that makes this character gp away?

Wouldn't be surprised if it's a glitch. I noticed there's a ton of them in the Thieves Guild missions. Just go and try to talk to him anyways even though he's not on the map. He's in the pawn shop next to the meadery if I'm not mistaken.

Maybe because he is in his shop. Have you checked to see if there is a quest marker pointing to a door?