The team said Monday that Bullock and Wilcox are both being held out for precautionary reasons.
Bullock is still rehabilitating the right quad soreness he had during last season, when he averaged 2.7 points and 1.3 rebounds in 43 games.
Wilcox has a right shoulder injury. The 6-foot-5 guard out of Washington was drafted 28th in the first round last month. He averaged 18.3 points, 3.7 rebounds and 2.5 assists in 32 games as a senior last season.
Coach Doc Rivers says the team wants to make sure both Bullock and Wilcox are healthy and ready for the start of training camp this fall.