might depend on who's getting married, i.e., 2 foreign nationals, 2 bulgarians, or one of each...but off the top of my head;
i know when i married a bulgarian, i had to supply a certificate of no-impediment, basically showing i wasn't already married, and also an official document stating that british law would recognise the marriage. these i had to get from my local registry office.
in bulgaria we both had to get a blood test, i suppose in case we had any nasty surprises in store.
we then had to provide all the above documentation, plus birth certificates to the british consul over there, who then issued a certificate giving the go-ahead.
i might well have missed something out, but if you want to send me a PM, i'll forward you some email information i gathered from relevant authorities when it still seemed a good idea (kidding obv - it was a great experience, i'm sure much better than it would have been here).