How much does it cost to deal with shoots keep coming up where the tree used to be?

Cheapest by a wide margin when added to the original removal — herbicide applied at the moment of the cut is a small line on a job already underway. Coming back later means a separate trip charge, and controlling established suckers gets priced by treated area and number of repeat visits rather than by tree. Suckers spread through lawn or into planting beds cost more than a tight ring on the stump, because treatment has to be selective around plants you are keeping. If the species is one of the aggressive ones, price the control as multiple visits from the start instead of expecting one.