Bulgaria has the the same visa rules as the rest of the Schengen area, however Bulgaria is not yet a schengen country, so a Bulgarian visa will not give you access to the Schengen area.
Visas are not required by visitors from the following countries for visit up to 90 days in a 6 month period: Albania, Andorra, Antigua and Barbuda, Argentina, Australia, Austria, Bahamas, Barbados, Belgium, Bosnia and Herzegovina, Brazil, Brunei, Bulgaria, Canada, Chile, Colombia, Costa Rica, Croatia, Cyprus, Czech Republic, Denmark, Dominica, El Salvador, Estonia, Finland, France, Germany, Greece, Grenada, Guatemala, Honduras, Hong Kong, Hungary, Iceland, Ireland, Israel, Italy, Japan, Kiribati, Latvia, Liechtenstein, Lithuania, Luxembourg, Macao, Macedonia, Malaysia, Malta, Marshall Islands, Mauritius, Mexico, Micronesia, Moldova, Monaco, Montenegro, Netherlands, New Zealand, Nicaragua, Norway, Palau, Panama, Paraguay, Peru, Poland, Portugal, Romania, Saint Kitts and Nevis, Saint Lucia, Saint Vincent and the Grenadines, Samoa, San Marino, Serbia, Seychelles, Singapore, Slovakia, Slovenia, South Korea, Spain, Sweden, Switzerland, Taiwan, Timor-Leste (East Timor), Tonga, Trinidad and Tobago, Tuvalu, United Arab Emirates, United Kingdom, United States, Uruguay, Vanuatu, Vatican City and Venezuela.
Visitors who have a valid Schengen visa can enter Bulgaria for up to 90 days with no visa.
Bulgaria visa information
Shengen Visa Information