Check out the Bulgarian embassy in London - Google finds it quite easily, there is information on there regarding visas and passports for travel to Bulgaria.
If in doubt e-mail them with your details, we got a detailed reply within 24 hours, or give them a call, e-mail addresses and numbers are on the website.
Just checked it out for you. No you don't need a visa on a US passport. You can go for 30 days as a visitor, same rules as a UK passport holder. Different story if you want to work or live in BG.