Answer:
Unlike some airlines, Greyhound does NOT allow pets on board, either in the passenger compartment or in the luggage compartment. Specifically, Greyhound's website states that:
"No dogs, cats, birds, or other animals will be transported. However, a service animal, trained for the purpose of accompanying a disabled person, will be permitted to travel with the disabled person at no additional charge.
Traveling With Your Service Animal
At Greyhound, customers with disabilities accompanied by a service animal are welcome. The service animal is the responsibility of its owner and must be under the control of its owner at all times (i.e., leash, harness or carrier). The service animal must ride in the bus within the customer's space. Service animals may not travel in the aisle or occupy a seat. Greyhound reserves the right to refuse passage to any animal that poses a direct threat to the health and safety of other customers, Greyhound personnel or contractors."
Source: http://greyhound.com/travel_information/bus.shtml