Thetrainline show a route via Three Bridges, which involves just one change but the National Rail timetable doesn't show this route at all. There is definitely a train from Portsmouth and Southsea at 16.16 arriving at 17.34 and then a train to Bedford at 17.55 but is there any reason why this route doesn't come up on the National Rail timetable? There seems to be plenty of time for connection as Three Bridges is quite a small station, I think? How come thetrainline and National Rail show different things anyway - don't they use the same data?