Technically there is a way to clear your name for half price, you have to make the Thieves Guild as strong as it used to be however, once that happens you should have several options for when the guards show up.
1) I am with the Guild will this cover it (Pay 1/2 of X from 4) 2) I am with the Guild how about you ignore this (pay Guard X amount in bribe, doesn't technically get rid of your bounty or at least never has in my experience, only useful if you murdered like 40 people) 3) I Submit, take me to prison. 4) I'll pay my bounty (pay X amount of gold) 5) I'd rather die than submit
Other options that sometimes show up after you have fled and returned to a hold.
(Persuade) Is this really worth your time?
I have only encountered it when my bounty was low. --- I saw a Mudcrab the other day, then I took an arrow to the knee.
This isn't related to the Thieves Guild btu it might help. If you have a really high bounty in any of the holds in Skyrim then when you're wandering around outside a town there is a chance a bounty hunter will come to kill you. If you pay him off I think your bounty in that area disappears.
However, I killed my bounty hunter after paying him off and I still have my bounty. --- Something better needs to be here.
There is also one more option if you happen to be Thane of a hold. You can ask the guards to ignore your crime. I had to use this option when I accidentally killed a bystander during a random dragon attack on Solitude.