How long does it take for paid bills to come off of a credit report?

You can review the Fair Credit Reporting Act for particulars, but generally speaking a paid bill will come off of your credit report 7.5 years after Date of Last Activity (DLA). In your case the DLA would be the last date your final payment was applied to the balance, paying it in full. If you are interested, I may be able to help you remove trade lines where the balance was paid in full. Let me know.