Bates went undrafted in the 1983 NFL Draft after he ran the 40-yard dash in a disappointing 4.8 seconds during the NFL Scouting Combine. He was selected by the New Jersey Generals in the 1983 USFL Territorial Draft, but he decided to sign as an undrafted free agent with the Dallas Cowboys, which had been his favorite team growing up. He was a long shot to make the team but he earned a roster spot. From the start he excelled on special teams, being named NFC special teams player of the year as a rookie.