Geeta bagged the silver in the 59-kg category after she failed to compete due to an injury in the final against China's Hui Li, while Bajrang lost to Devin Carter of Hokie Mat Club (1-1,0-2,3-0) in the 60-kg competition of the men's freestyle.
Sandeep Tomar (55kg) was the bronze medal winner in free style event, being held at Colorado Springs.
Amit Kumar, the gold medal winner in 55-kg category last year, failed to defend his title as he lost to Mark McKnight in the second round bout.
Silver medallist at the London Olympics, Sushil Kumar, the other gold medal winner for India in the last edition, had pulled out of the tournament due to an injury.