Investigators say that Bughman was arrested at his parents' home in Apple Valley after the students came forward and reported the alleged abuse.
Investigators say the crimes against the victims include rape, oral copulation of a minor, penetration of foreign objects and other sexual abuse charges. These crimes allegedly happened over the span of 13 years. Authorities say the first alleged victim came forward in April.
Bughman was scheduled to be arraigned Friday, but his hearing was postponed until Monday.
The school district says that employees undergo thorough background checks.
"Up until this point, he has been a well-respected teacher. We've maintained rigorous and very high standards in terms of our hiring practices," said Dean Conklin, the superintendent of Duarte Unified School District.
The district has notified parents about the investigation. The Los Angeles County Sheriff's Department says investigators received credible information from the victims.
"One of the victims was a second grader. These females range from ages 7 to 14," said Steve Whitmore with the sheriff's department. "We believe that there may be victims as far back as 1993."
"A student initially came forward to the principal. We immediately contacted authorities. They came in and at that point essentially took over," said Conklin. "Mr. Bughman was placed on leave at the time as required by law."
Investigators want to know if there are other victims who have yet to come forward. If you have any information regarding this case, you're urged to call the L.A. County Sheriff's Department at 1-866-247-5877.
Bughman is being held on $2.1 million bail, and faces life in prison if convicted.