In 1989, Bieniemy was ticketed in Westminster, Colorado for driving a defective vehicle, and in Aurora, Colorado for speeding. In October 1990, Bieniemy's license was suspended for a year after another traffic violation. On March 21, 1991, Bieniemy was caught speeding and driving with suspended license on I-70 near Rifle, Colorado, going 92 mph in a 65 mph zone. On April 17, 1991, Bieniemy failed to appear in court on charges relating to the March 21 incident. A bench warrant was issued in Colorado for his arrest on April 23, 1991, two days after he was drafted in the 1991 NFL Draft.