if you are talking 250 quid for a bumper...
1) from places local to me to get a full bumper painted you are talking about £150, especially something as big as a BMW bumper.
2) then the bodyshop will be adding more on top of that for repair work, which i would say at least £50 considering the amount of work needed to repair such a big hole.
3) from experience, large areas filled in like that, the isopon/filler can sometimes sink
for the sake of an extra few quid I would rather get a bumper, then you will know that it wont have any imperfections.
Just curious, if you know it was some idiot reversed into the car, why isnt the idiot paying for it anyway?