You do not say what nationality you are. An "Indefinite Leave to Remain" is exactly that. You may live in England for an extended period without reference to the authorities. You will be allowed back into the UK (make sure you have enough paperwork with you to establish your status, and don't lose it in Bulgaria).
So the only problem is whether the Bulgarians will let you in (and back out). Check with them for your nationality and status.
