Polishing to remove stains on dental bonding? Is this an option? What are the costs?

Hello! I have a gap between my front two teeth and I had them bonded together to cover the gap about 8 years ago. Since then, the material used to bond them picks up stains like crazy and has caused one of my teeth to become obviously discolored. I'm looking for a solution to removing the discoloration from the tooth. I know getting a veneer is an option, but I can't really afford that right now. I've read that my dentist can polish the teeth and remove the stains, is this true? Cost?