I boarded Greyhound at a stop (not a terminal) about 18 months ago and had the exact experience user4556274 described in her comment:
The driver got off the bus and opened the luggage compartment doors. People started chucking their bags under there while he checked tickets for all the passengers. Once a person's ticket was checked (s)he was allowed to board.
This happened at every one of the 6,723 stops on the 12 day journey that should have taken about 3 hours.
slight exaggeration - not a fan of bus travel. :(
The trip ended at a terminal which I returned to 10 days later in order to make the journey back home. It was the exact same process, just at a terminal instead of a "stop". There was no baggage check in process like there is at an airport, just the same curbside process with the exception of there being multiple "curbsides" all one right next to the other.