Sorry to disagree, but buying here and registering IS possible, otherwise how would folks from a country outside Bulgaria ever do it? I recently sold a vehicle to a Romanian lad who came down from Bucherest for a months holiday,saw the car, bought the car, insured in his name, drove it home and phoned me three weeks later and thanked me for a hassle free sale.
For what it's worth, I drive a RHD Jeep and a LHD Nissan Patrol these days and like any competent driver, have no problems swapping from one to the other.