The Pretoria franchise is coming off a difficult 28-7 loss at the hands of Ulster and now face the prospect of playing their next three matches without the superstar No.10.
Bulls coach Johann Ackermann revealed that Pollard is set to return to South Africa to witness the birth of his second child, due around 20 October. As such, the double World Cup winner in set to miss the upcoming clashes against Connacht and Glasgow Warriors.
Also in doubt is the next URC fixture against the Lions. The Springboks face Wales in Cardiff on the same day, 29 November, and Pollard will in all likelihood be with the Boks.
"I tried to stick to my word, which was that he was always going to play just one game," said Ackermann.
"His wife is due [to give birth] on October 20, so he wants to return home in time for the occasion. There's always the possibility that the baby can arrive earlier, so he will be with his wife and his family.
"We don't know which players will be available for the clash against the Lions because the Boks are playing on the same day. We'll have to see who is available to play."
In Pollard's absence, Ackermann is set to lean on Johan Goosen, who has had a torrid time with injury. Failing his match fitness, the Bulls may have to name Bok centurion Willie le Roux at flyhalf.
"Johan joined us on the second day of the tour, and on the second day of training, he felt a bit of discomfort in his calf," continued the coach.
"We will make a final decision on his availability tomorrow [Monday] to play against Connacht when we start training.
"We are currently halfway on our trip to Connacht, but we will reassess his availability."