The actions came after a tough Sunday for the veteran driver at Texas Motor Speedway during which he gave "the finger" to officials while in the pits to serve a drive-through penalty.
Busch ended in 32nd place.
The fiery driver had also angrily stormed out of a press conference Saturday following his close loss to Carl Edwards in last weekend's Nationwide Series event.
"I accept NASCAR's penalty and realize what I did during Sunday's race at Texas was inappropriate," Busch said in a statement. "Even in my relatively short time here in NASCAR, it's pretty obvious to everyone that I wear my emotions on my sleeve.
"Sometimes that passion has allowed me to find that little something extra I needed to win, and other times it's made me cross the line. Sunday at Texas was one of those days."