Unfortunately, most carriers do not allow pets on buses or trains.  

There are, however, a few exceptions:

Your furry is a certified service animal: in which case please contact the carrier your wish to travel on for more information. 

Most carriers will accept service animals. A “service animal” is any guide dog, signal dog, or other animal individually trained to do work or perform tasks for the benefit of an individual with a disability, including, but not limited to, guiding individuals with impaired vision, alerting individuals with impaired hearing to intruders or sounds, providing minimal protection or rescue work, pulling a wheelchair, or fetching dropped items.

Emotional support and comfort animals are not considered service animals under the ADA. 

Exceptions are for trips scheduled with train carriers (additional fees may be required and "seating" may be limited) and for travel with bus carriers that service certain airports. Here are a few:

Via Rail Train (Canada): 

Amtrak Train (US and Canada):

Peter Pan Bus (to/from Logan Airport, T.F.Green Airport)
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The pet must be transported in a suitable container for the duration of the trip and the pet/container must be confined to the seating area of the customer (ie: not take up the space of another seat or take space in the bus aisle).

We still do recommend that you check with the carrier you will be traveling directly, especially for information regarding smaller animals.

Safe travels!