Here is what is written on the latest Foreign & Commonwealth Office Country Advice for Bulgaria:
British citizens holding valid passports can enter Bulgaria for up 3 months, and have the right to stay longer if exercising an EU Treaty right, although you will need to register with the police. Prior to travelling you should ensure that your passport has a validity of six months beyond the end of your intended stay
. Damaged passports will not be accepted."
It is always good to check this website before travelling as it is regularly updated and has the latest important information for the country. The link is: