A statute of limitations is a deadline for filing a lawsuit. It is not a deadline for collecting a debt. A creditor can, theoretically, attempt to collect a debt for the rest of your life by continuing to ask for it as long as the creditor doesn't violate any fair credit laws.
California has it's own Fair Debt Collections Practices Act that does apply to the original creditor as well as collection agencies:
http://leginfo.legislature.ca.gov/fa...pter=&article=
However, I don't see anything in the prohibited acts that prevents a creditor from saying "You want something from me, you pay what you owe."
If you cannot convince the creditor that you don't owe the $135.77 and don't want to pay it then the ability to use bill pay is not in your future and you'll have to pay your bills by writing checks or using your credit card and paying your credit card bill in full to avoid paying outrageous interest rates.