Bowe and one of his two passengers were arrested Sunday night, WDAF-TV reported.
Police in Riverside said Bowe was pulled over after an officer observed him going 48 mph in a 35-mph zone. The officer said that he noticed an odor of marijuana when he talked to Bowe.
The officer said a K-9 dog alerted on the vehicle and a subsequent search turned up a container in a backpack that contained a small amount of marijuana. George Thompson, a passenger in the car, said the backpack was his and was also found to have two marijuana cigarettes.
Bowe was charged with speeding and marijuana possession, with bail set at $750, while Thompson faced only the drug charge with $500 bail. The second passenger, who was not charged, posted bail for both men.
The Chiefs drafted Bowe, 29, in 2007.