Yes, contact (or look on website) for all airlines flying non charter flights to bg. Then do some sums comparing total costs of tickets and pet deal. It'sbill did this last year and we went to the airport to give him a hand, it was a doodle. The airport staff couldn't be more helpful. He went Bulgaria Air from manchester. You need to get forms from defra, and make sure your vet is an approved export vet, if not your vet will be able to tell you who in your area is. You need tests for brucellosis which may take some time and your general vaccinations need to be up to date. Pets have to be microchipped as well. All in all, nothing too hard to do.
Let me know if you need any more info