Now that Bulgaria is part of the European Union it is much easier and cheaper for British people to establish residency here. The days of needing to prove a reason to be in the county are gone and it is no longer essential to be paying health care or pension contributions in Bulgaria, or to appear to be running a company.
In essence you need to prove that you are working in Bulgaria and/or have sufficient means to support yourself. You will need to demonstrate that you have somewhere to live and at least in the early years of your residency that you will not be a burden on the Bulgarian social security system.
Although the system is now much simpler than it was, there are still a variety of documents to be gathered together and some choices you need to make in deciding your grounds for residency.
Some people, particularly those with experience of living abroad and some basic language skills will be able to complete the process themselves; others will find it useful to have someone to guide them through the process. If you have a Bulgarian friend who speaks English take them along.
If you want someone more official there's a very helpful solicitor in the area:
Attorney At Law