Those trains have dedicated bike spaces and you can't take it in the normal carriage. Booking a bike space is free and you can do it online if you book your ticket through East Coast. Otherwise if you book through FGW (or anyone else) you'll have to phone up.
I have taken a bike on those trains plenty of times without booking, but did get caught out and have to wait an hour for another train once. If the bike spaces are all taken then it's up to the guard to decide whether you can take it on, unless you have a bike reservation in which case they will find space regardless of how many bikes are already on the train.
Those trains have dedicated bike spaces and you can't take it in the normal carriage. Booking a bike space is free and you can do it online if you book your ticket through East Coast. Otherwise if you book through FGW (or anyone else) you'll have to phone up.
I have taken a bike on those trains plenty of times without booking, but did get caught out and have to wait an hour for another train once. If the bike spaces are all taken then it's up to the guard to decide whether you can take it on, unless you have a bike reservation in which case they will find space regardless of how many bikes are already on the train.