How long does a contractor have to bill for services rendered?

The maximum time the contractor would have to try to collect payment--i.e. bill--is something a bit less than five (5) years, as defined by the statute of limitations. In your state, a lawsuit to recover money owed per an agreement (written or oral) to perform work must be initiated within five years; therefore, the contractor would effectively need to bill in somewhat less time than that, so that if not paid, he could file a lawsuit.

But that is somewhat more theoretical and practical, since there are legal doctorines (e.g. laches; estoppel) that can prevent someone from bringing a legal claim if he waited for an unreasonably long time without any good reason for the wait; a contractor who tried to bill for the first time 4 1/2 years after the fact could easily have his lawsuit thrown out or dismissed.

That said, a contractor could succesfully bill more than a year after the work. There is no hard-and-fast deadline in the law, other than, as discussed above, the statute of limitations as affected by legal doctrines that make it more difficult to pursue a claim after an unreasonable delay.

Of course, if there is anything in the contract or agreement defining when an invoice, etc. should be submitted, that contractual term would control, and the contractor would need to bill within that time frame.