I have completed all the thieves guild quests and have access to both S'Krivva and Armand. I have a bounty on my head and wish to remove it, however, every time I go to one of them, I get stopped by guards first. This isn't a huge problem because I can resist arrest and run to S'Krivva and Armand and clear my bounty.

The problem arises after I clear my bounty. The guards who originally stopped me are still attacking me. Worse yet, more guards join in on the fight and my bounty goes from 0 to 40 and then it turns into a never ending cycle. How can I clear my bounty without the guards seeing me or attacking me?

Sneak.

Seriously (no offense meant, but seriously) any thief that can't get to Armand without being seen by a guard is a pretty poor thief.

Yeah, he's right. To get to Armand without being seen, put your blue marker on the map where he usually stands, then approach from a south-east angle, swimming across the bay.
S'krivva is harder, because she's in the city, so try Armand first.

If, as you say, you have a clear bounty and are still being attacked, you may have a bug of some sorts. Make sure you have no theiving mods etc installed, otherwise, find your save file, copy it to a safe place on your PC and reinstall Oblivion. Usually works for bugs.

As soon as you pay the Doyen, surrender (yield: that's block and talk) to the guard. He'll stop attacking, and no further fines will be incurred if you don't fight back before yielding.

Thanks that worked! And as far as being a bad thief, yes, I am. I just transferred from Morrowind a few days ago and it's taking me a while to get adjusted. Guards can actually follow you into houses!

Not only that, they can respond to cries for help that come from within a house, if they're outside.

It can take some time getting used to Oblivion, after Morrowind, the AI in this game is much more realistic.

http://www.uesp.net/wiki/Oblivion:Oblivion_for_Morrowind_players