The Three Lions led 2-0 through early goals from Marcus Rashford and Ross Barkley when play was first stopped and an announcement made to supporters that the game could be suspended if offensive chanting continued.
Once restarted, England quickly made it 3-0 through Barkley. Then play was interrupted a second time as Croatian referee Ivan Bebek held discussions with players and coaching staff from both sides.
In total, played was halted for six minutes.
Raheem Sterling added a fourth England goal before half-time.
A section of 5,000 seats at the Vasil Levski National Stadium was already closed for the game after racism during games against Kosovo and the Czech Republic in June.
Sterling was also the subject of racist abuse from a Bulgarian fan when the sides met last month in England's 4-0 win at Wembley.
On the eve of the match, Bulgaria manager Krasimir Balakov claimed that there is a bigger problem with racism in English football than in his country.
"In the Bulgarian championship, we have a lot of players of different ethnicities and skin colour," said Balakov.
"I don't think that we have this big problem like, for example, England do."
After several England players suffered racist abuse in a qualifier away to Montenegro in March, Gareth Southgate had prepared his side to follow UEFA's three-step protocol for reporting racist incidents that can lead to matches being abandoned.