Bedford definitely has a club. I believe the clubhouse and track are somewhat south of Bedford. It's 45+ years since I was a member so I can't tell you anything about the demeanour of the club.
There is a track and club, just a few miles up the A5, in south Milton Keynes. It is right next to the pub/hotel (the big windmill one) by Caldecotte lake. I think there is a website for them.
Yes, as above you have a choice of Bedford and Milton Keynes. Luton is a good boat club. You will be welcome for days out at St Albans and North London clubs too.