Bedford never ran a competitive marathon during his 'career' - he concentrated on track and cross country, with best times of around 13:16/5000m, and 27:30/10.000. He ran some road relays for his club (Shaftesbury), but do not think he ever races further than 5 miles on the road.
Bedford lacked basic speed (around 57 for a 'flat out' 400), but his strength gave him the ability to run very close to his top speed for long periods of time.
His career did not last long, because he really pushed the envelope (mileage wise) in training, with some weeks approaching 200 miles a week, most of it on the roads.
The 10.000 record came about in an interesting way. Bedford had been injured for months and months, and nobody expected the record, but all the previous work and training paid off, and the involuntary rest from the injury actually helped Bedford as it gave him an extra freshness with which to beat the world mark.
Bedford never minces his words. On once occasion Jon Brown expressed a wish to run the London Marathon in around 2:13, which made Bedford say 'why would anyone want to deliberately run that slow!' or words to that effect. Brown and Bedford had a 'falling out' at London for a couple of years with these issues and financial ones, but, fortunately, are now back on speaking terms.
I also recall how rude Bedford was to the invited Mexican runners at the Crystal Palace Grand Prix in around 1978. The Mexicans were very upset, despite having a bunch of sub. '28' minute 10.000 runners.
He is just a very honest guy in the sense that he always speaks his mind, but this can upset some people.