The bus went off the shoulder of an Interstate 10 off-ramp in Baldwin Park shortly after 4:30 a.m., California Highway Patrol Officer Christian Cracraft said.
The bus wheels went into a small drainage ditch and it came to rest against a fence and light pole but remain upright.
"The bus tried to get on the ramp to exit, but he come too fast. He can't control the bus," passenger Eduardo Magana told KCBS-TV.
Eleven people received minor injuries and two received moderate injuries, the station reported, citing the Los Angeles County Fire Department.
KNX-Am reported that one person had a broken arm.
Nearly 40 people were on board the bus, which was returning from the Fantasy Springs Resort Casino in Indio. They were briefly trapped by a blocked door before rescuers freed them.
The freeway remained open.
The accident came four days after three bus crashes on rain-slick Southern California freeways killed two people and injured dozens more.
Khang Tieu of Midway City, 91, died Thursday night, eight hours after a bus returning from a San Diego County casino overturned on Interstate 15 in Corona.
Some two dozen people were hurt. The CHP said the bus was doing 65 mph - an unsafe speed for the rain-slick roadway.
At about the same time as that crash but about 50 miles away, a bus heading to another San Diego County casino overturned on the freeway near Fallbrook.
Tayde Murguia, 64, of Los Angeles was killed and 19 others were hurt.
At least 14 people were hurt Thursday morning near Perris in Riverside County. A county Riverside Transit Agency bus on State Route 74 slid sideways and hit a car traveling in the opposite direction, which then was hit by a tow truck, the CHP said.
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