As a permanent resident of Bulgaria, can I travel to the USA and Canada?
Currently, the USA and Bulgaria do not have a Visa-waiver agreement established.  Any Bulgaria travelers planning on visiting the United States must first obtain a visa, either a nonimmigrant visa for temporary stay or an immigrant visa for permanent residence.
As to Canada, Bulgarian passport grants travelers visa-free entry into Canada. Instead of a visa, all travelers need is an Electronic Travel Authorization (eTA). An eTA is an entry requirement for visa-exempt foreign nationals traveling to Canada by air. It is electronically linked to a traveler’s passport and is valid for up to five years or until the passport expires, whichever comes first.  With a valid eTA, you can travel to Canada as often as you want for short stays (normally for up to six months at a time).