Bobby Babcock was born in Agincourt, Ontario on August 3, 1968. He played his junior hockey with the Sault Ste. Marie Greyhounds and the Cornwall Royals before turning professional in the Washington Capitals organization. The Capitals had selected Babcock in the 1986 NHL Entry draft and he joined their American Hockey League affiliate in Baltimore for the 1989-90 season. Babcock, a tough, physical defenseman, registered just four assists in 67 games that year but piled up 249 penalty minutes. The next year, Babcock got a one-game look from the Capitals.
Babcock's time in the minors was very limited as a result of injuries sustained from his style of play. He played just 38 games that year with the Baltimore Skipjacks. The next season, 1991-92, he was limited to only 26 contests. In 1992-93, the Capitals again gave him a one-game trial, but he didn't stick with the team beyond that.
The rest of his season was split between the Skipjacks and the Hampton Roads Admirals of the East Coast Hockey League. Babcock joined the Binghamton Rangers of the AHL for the 1993-94 season. He played just 20 games with them and then retired from professional hockey.