What is the best size dirt bike fro an 11 year old boy?

It depends on how tall the boy is. Average 11 year old goes about 52" or 4 feet 3 inches (or so). You can get him a 20" bike (20" being the diameter of the rim). If he doesn't seem to fit on it, you'll be able to lower the seat so that he does fit, and believe me, he'll grow into it within the next couple months.