Check out Study Bulgarian Online for a comprehensive explanation of the alphabet, grammar and basic vocabulary. The site is free and will give you the necessary introduction to delve deeper into the language.
Try Easy Bulgarian for a more interactive online course. They offer continuing courses, one-on-one tutoring and translation services. The service is not free, but it will carry you further than you could go on your own.
Visit I Learn Bulgarian for another introduction to the basic necessities of the Bulgarian language. They offer several written sections to get you started, and offer a forum, so you can talk to other students of the language. Nothing helps motivate like having a study-buddy.
Try learn Bulgarian Easily to receive eight free video lessons and the opportunity to learn more. The site also offers an English-Bulgarian online dictionary, which is free to use and allows searching for specific words.