Bush did not play in the second half of the Saints' Sunday game against Carolina, won by the Panthers 30-7, after aggravating an injury to his left knee.
He was hurt on a punt return late in the first half.
The Saints will play the San Diego Chargers Oct. 26 in London.
"We're going to look at his meniscus, his left knee, a little bit more," Payton said. "There's a chance that he won't make this trip and we fly him to (Dr. James) Andrews for a scope, there's a good chance that's going to happen."