You may have already bought your ticket on Greyhound, but let me recommend you find just about any other form of transportation to travel! I've always had bad experiences on their bus lines. There are other bus lines out there, such as bus lines that run between Chinatowns. Perhaps there is an Amtrak station near where you want to go.
If you ordered your tickets online you need to bring id so that they can identify you as the purchaser. You also need to bring the confirmation from the online bus ticket purchase. If you did not order online than no you don't need an id but it's always good to have one.