Bicknell was named the head coach of the Barcelona Dragons at their inception in 1991, and served there until October 2003, when he was named head coach of the Scottish Claymores. He has an overall record of 59–55 in his NFL Europe career. Bicknell has made four World Bowl appearances, and has been to three title games in the past six years. In 1991, he led the Barcelona Dragons to an 8–2 mark and a berth in the first World Bowl. In 1997, his Dragons won the first half of the season and went on to win World Bowl '97 in Barcelona. In 1999, the Dragons posted a league-best 7–3 mark before losing to Frankfurt in the World Bowl. Also posted a league-best 8–2 record in 2001 before losing World Bowl IX to the Berlin Thunder in Amsterdam. On March 28, 2007, Bicknell stepped down as head coach of the Hamburg Sea Devils, citing health issues as the reason for his resignation.
Bicknell is nicknamed "Cowboy Jack" because of his love for country music and horse riding. He and his wife, Lois, have three children, Jack, Jr., Wendy and Bob and five grandchildren. Both of his sons played for him at Boston College and are currently coaches in the National Football League.