Innanzi
IME trains to Oxford from PDTN don't require booking, but do get busy on a Sunday evening back to London, which can make taking bikes a bit ... hassleatious. Not sure about now but the bike spot was pretty small when I last used one about two or three years ago.
Anyhow I'm sure it'll probably be fine. The mainline fast trains would probably take you on spec', you can just pick up a bike reservation at the ticket office when you're at the station.
Innanzi
IME trains to Oxford from PDTN don't require booking, but do get busy on a Sunday evening back to London, which can make taking bikes a bit ... hassleatious. Not sure about now but the bike spot was pretty small when I last used one about two or three years ago.
Anyhow I'm sure it'll probably be fine. The mainline fast trains would probably take you on spec', you can just pick up a bike reservation at the ticket office when you're at the station.
Have fun there, doing anything nice?
edit: and ^ what snottyotter said!