Unless the bike has had an insurance claim made on it, it wont be on the insurance catagoration register. It will however be marked as stolen on pnc if its been reported to the police as stolen and you dont tell them you have got it back. If you dont tell them soon as you tax it dvla will tell them as stolen bike has been taxed.
What were you doing buying your own bike back anyway ? You should have went to see it, checked the frame number, walked away and rang the bizzyz and they would have got it back for free and removed the stolen marker from the pnc.