He was ticketed for speeding, improperly signaling and not carrying proof of insurance during a March stop in his hometown of Portland, Ore. Police said he was driving a BMW 91 mph in a 55 mph zone.
In December 2011, Suh lost control of a car and crashed into a drinking fountain and tree in Portland. A woman has filed a civil lawsuit seeking $1 million from Suh in the crash.
He also was involved in a traffic accident last month in Dearborn. Police in the Detroit suburb said the accident was minor and fault could not be determined. When Suh played at Nebraska he pleaded guilty to negligent driving and paid a $60 fine after crashing into three parked cars.
Schwartz chuckled when asked if it might benefit Suh to hire a driver.
"Honestly, I think it would be best for every single player in the NFL to have a driver," Schwartz said. "I don't know if that's always feasible and things like that, but I think there are a lot of situations that can be avoided ... if you have a driver. And it just takes something else off your radar, and he certainly is in a very fortunate position that he could afford something like that.
"We want all our players to be good citizens off the field, to be safe drivers, to pay parking tickets — all those things. That's just all part of being a member of society."
Associated Press writer David Runk and AP Sports Writers Larry Lage and Noah Trister contributed to this report.