Ok, so basically I became a member of the Thieves guild so that I could pay off the guards for a good price to remove my bounty. Unfortunately... it's not working. It works perfectly fine in Riften, but it won't work in Windhelm... where I actually need it to work. The dialogue option simply does not appear. Why is this? Is it a bug? What's the deal?

You cant simply join the thieves guild and pay off your debt like you could in Oblivion. I'm pretty sure you have to talk to vex to do different jobs and eventually you'll get a special job for a city. Once that job is complete, and the Thieves Guild has influence in that city, THEN you can pay off your debt.

Hmmm... That makes sense, I suppose. I'll give it a shot.