To purchase a ticket all you need is a credit card, but to board the bus at the terminal, you should have the hard copy of the ticket along with a government issued ID card like Driver's license or a state ID.
When I took the Bus from Texas to Florida, they required a Driver's License or State ID, in addition to proof of the Ticket. They also now do spot checks on the buses, where police come on board to check ID.. And Greyhound requires the Ticket to have the same name of the passenger...
As long as you have the credit card the purchase is made with to present at the terminal, just incase you don't print your ticket, none. There are fees for will call tickets and am id is needed for those unless the purchaser sets up a pin for the rider which will serve as an ID.
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