Bickell was a member of the Bantam All-Ontario champions Toronto Red Wings with future Chicago Blackhawk teammate Dave Bolland.

Bickell later made his NHL debut on April 5, 2007, where he scored his first goal against Chris Osgood of the Detroit Red Wings.

This would cause Bickell to miss the next 29 games for the IceHogs before returning to the lineup on March 7, 2009, in a 4–3 SO loss to the Peoria Rivermen.

[9] Three weeks later on March 28, however, Bickell suffered an eye injury in a 3–2 loss to the San Antonio Rampage after getting hit in the face with a puck from a slapshot by teammate Jordan Hendry, causing him to miss five more contests before returning to the IceHogs lineup once more on April 10 in a 2–1 win over the Peoria Rivermen.

[11] On December 27, Bickell recorded his first NHL assist on a goal scored by John Madden in a 5–4 win against the Nashville Predators.

[21] Bickell's offensive production dropped during the 2011–12 campaign, where he only tallied nine goals and 15 assists for 24 points in 71 games while continuing to be a staple on the Hawks' third line with Dave Bolland and Michael Frolík.

He recorded the game-tying goal against Boston Bruins goaltender Tuukka Rask during Game 6 of the Stanley Cup Finals on June 24, 2013.

[25] After the playoffs were over, Bickell revealed he had played through a torn MCL that was originally sustained in Game 5 of the Western Conference Finals on June 8 against the defending Stanley Cup champion Los Angeles Kings.

[26] On June 30, 2013, the Blackhawks awarded Bickell's strong postseason performance with a four-year, $16 million contract that goes through until the 2016–17 season.

[27] On November 19, Bickell suffered an undisclosed lower-body injury in a 5–1 loss to the Colorado Avalanche after sliding feet first into the net.

[29][30] Bickell then missed six more games after sustaining an undisclosed upper body injury on March 19, 2014 against the St. Louis Blues before returning to the lineup on April 3, against the Minnesota Wild.

Despite the injury-filled regular season, Bickell replicated his productivity from a year prior on another lengthy playoff run during the 2014 playoffs while playing on the first line with Jonathan Toews and Marián Hossa[32] which saw the Blackhawks go to the Western Conference Finals against the Los Angeles Kings for the second straight year, which would see the eventual Stanley Cup champion Kings win the series in seven games, one win short from another appearance in the Stanley Cup Finals.

[39] Bickell was unable to consistently perform due to health-related issues and spent much of the season with the Rockford IceHogs of the American Hockey League.

[40] Bickell skated in 25 games for the Blackhawks and was goalless but recorded two assists and points while playing mostly on the fourth line.

[50] Bickell returned to the Hurricanes on April 4 in a 5–3 loss against the Minnesota Wild, and skated in his first NHL game since leaving for MS treatment in mid-November.

[58] Bickell began experiencing symptoms of vertigo that forced him to miss the first two games of the 2015 Stanley Cup Finals.

[61] In early-November 2016, shortly into the 2016–17 season, Bickell began experiencing an unexplained pain in his shoulder and leg that caused him to miss multiple games.

"[63] Ron Francis, the Hurricanes' general manager, stated that Bickell would take an indefinite amount of time off from hockey to receive treatment for his condition.

[64] While Bickell ultimately returned to Hurricanes towards the end of the 2016–17 season in April 2017, he announced he would retire from playing to focus on his MS treatment.