gotta say though, while looking up how to get to cumberland from NYC, I didn't find any trains on amtrak website from NYC to Washington DC that have the bicycle icon next to it.
However it does have the bicycle icon next to the transfer from DC to Cumberland. Not sure if that means if no bikes are allowed on NYC - DC section, or if you just cant book in advnce.
It's easy to take a bike on BoltBus which operates between NY & DC, and tickets are a helluva lot cheaper than Amtrak.