Obviously the holiday is more important to you than any ceremony regarding marriage vows because you booked that before knowing anything about whether it is possible. Not being an expert, but I guess that the marriage vow renewal doesnt have any formal legal significance, but is just a nice thing to do. (I notice in your post that you didnt indicate what branch of religion you married under, or whether it was a civil ceremony). Bulgaria will also have a different outlook towards things than we do. Even if you could translate what it was you wanted done, they might just look at you blankly. One avenue would be to see if there is any presence on the www. of the Anglican church in Bulgaria. I would be surprised if there wasnt something in Sofia or Bourgas. This assumes that you were married C of E, but if not just do the same for your religion. If you had a civil ceremony, then the first thing to find out is if their are such things as civil marriage ceremonies in Bulgaria. There must be practising vicars/ministers or whatever in Bulgaria who would be willing to informally attend a private ceremony. The key is finding them.
Also, read Lonely Planet and Rough Guide as they will certainly have contact info for various churches in Bulgaria.
To save a lot of hassle, get the ceremony done in the Uk and have a honeymoon renewal!!!!!