I am a dual British-Bulgarian citizen and I was recently denied a Russian visa on my British passport. I had applied through a tourist agency and they did not understand the reasons for the denial either.
It was even more difficult for me to understand. It had something to do with my British citizenship and passport. The Russian consulate in Varna said that the UK and Russia had not signed a certain agreement that would have allowed the Russian consulate to issue me a visa?! To complicate the matter further, the Russian consulate associated me with somebody they had had telephone conversations with. I had never called the Russian Consulate in Varna.
I prefer to travel on my British passport. I do not hold a valid Bulgarian passport.
I contacted the British Embassy in Sofia asking them to uphold my right as a British citizen to travel on my British passport. If nothing would help to resolve the issue, I asked the embassy to stop issuing British visas to Russian citizens in Bulgaria.
I got a reply from the embassy that they could not interfere with the visa policies of a foreign country.
So, if you are a British citizen living in Bulgaria and want to visit Russia, be prepared for surprises.
R. P., Veliko Tarnovo