Amtrak, the heavily subsidized rail operator, will carry your firearm, but is not eager to carry your bicycle. Nor will they carry your dog or cat. Amtrak won’t permit any pets on-board at all, except for guide dogs.
The only options for pet owners are driving, flying, or pet boarding. In the case of flying, pet owners are understandably skittish about sending fido through the airport luggage system, or in the cargo hold. So this is one market where Amtrak could be hugely competitive against the airlines — if only Amtrak management weren’t so sclerotic.