In reply to Mr west:
There isn't anywhere to boulder outside near Bedford/Milton Keynes except on manmade structures in desperation. You have to travel for anything decent.
There's bridges in Bromham, Clifton Reynes and Wolverton that people have climbed on but they're a bit dusty and tend to feature loose rock and mediocre climbing (and the Clifton Reynes bridge has a landowner who isn't at all keen on people climbing there). I used to live a 1 mile walk from Clifton Reynes and still never used to climb there.
There is also a slate statue in Campbell Park Gnomon, Milton Keynes which can be entertaining for a visit on a sunny evening but you wouldn't climb on it if there were any decent options and you're probably better off just staying indoors and climbing at Big Rock.
I've heard rumours of some rocks in the woods behind the play park in Emberton park. But if there was anything any good there, I would have heard more about it.
The closest worthwhile places to boulder outside are Leicestershire (about an hour North) and the Peak District/Churnet/Eastern limestone (about 1.5-2 hours North).
Leicestershire has Forest Rock which is great for overhanging burly bouldering at 7A (V6) and above. There isn't much that's easier than that though. Or there's Cademan Wood and Broad Hill which has more easier things. Cademan has a few good quality problems but the average quality is poor; there's a lot of eliminate, lowball problems there and the rock can be very sharp. Cademan is worth visiting once or twice if you don't have time to go to the Peak District but you're generally better off keeping on driving until you get to the Peak.
Day trips or weekend trips to the Peak District and other further afield destinations are your best option. There's enough good quality bouldering in the Peak District at all grades to last a lifetime.