Bugg was born to Jim and Kerry Bugg (née Ramage) in Melbourne, Victoria; and played his junior football career with the Gembrook-Cockatoo Junior Football Club and Beaconsfield Football Club before joining the Gippsland Power in the TAC Cup as a bottom-aged player in 2010 where he played eight matches and kicked two goals, including the grand final loss against the Calder Cannons. He received state honours in 2009 when he played for Vic Country in the under 16 championships, and received a scholarship within the prestigious AIS/AFL Academy as part of their 2009 intake. He was again selected for Vic Country in 2010, this time in the AFL Under 18 Championships and played his best game for the series against NSW/ACT, where he was named in the best players. In October 2010, he signed a three-year contract with the Greater Western Sydney Giants (GWS) as an underage recruit, which was a special recruitment process allowed by the AFL Commission where GWS could sign twelve players born between January and April 1993. As GWS wouldn’t compete in the Australian Football League (AFL) until 2012, he moved to Melbourne in 2011 to complete year twelve at Caulfield Grammar School as a boarder.

After a strong pre-season in 2014 where he won the club three-kilometre time trial, Bugg played the first six matches of the season before he was omitted for the round seven match against Port Adelaide at Manuka Oval. He returned to the senior side for the forty-five point win against Brisbane at the Gabba in round thirteen where he was a late replacement for Aidan Corr. During the match, he was involved in a marking contest where his hip collided with Jonathan Brown’s head, which subsequently forced Brown into retirement after receiving too many head knocks. After receiving the reputation of being “one of the best nigglers in the competition”, he was involved an incident in round fifteen where he bumped Sydney captain, Kieren Jack, which drew condemnation from the public, in particular from Australian Football Hall of Fame member, Tony Shaw who described the bump as “pretty ordinary”. He was involved in further incidents, which saw both St Kilda’s, Maverick Weller and Fremantle’s, Hayden Ballantyne suspended for striking him, and North Melbourne’s, Sam Gibson suspended for rough conduct.

After playing every match in the 2016 NAB Challenge and being named as one of the “eye-catching” players during the pre-season by AFL Media, Bugg made his debut for Melbourne in the opening round of the season against his old side, Greater Western Sydney at the Melbourne Cricket Ground in a two-point win. He drew negative attention during the 33-point win against Richmond at the Melbourne Cricket Ground in the annual Anzac Day eve match for two separate incidents, the first where he pushed Jack Riewoldt when he was injured and Bugg received a $1000 fine from the match review panel for “making contact with an injured player”. The second incident was his celebration after kicking his only goal for the match, where he put his finger to his mouth to silence the Richmond cheer squad with a wink, which drew displeasure from the commentators. He later apologised for both incidents. He played every match for the season until the round 16 match against Fremantle at TIO Stadium, and played in the Victorian Football League (VFL) for Melbourne’s affiliate team, the Casey Scorpions, before returning to the senior side for the 29-point win against Hawthorn at the Melbourne Cricket Ground in round 20 and played the remainder of the season in the seniors. He played eighteen matches in his first season for Melbourne and finished seventeenth in the best and fairest count.

In 2017, during a game against the Sydney Swans, he struck Callum Mills in the face in the opening stages of the match. The incident happened four minutes into the game and behind play. Bugg was reported immediately and later received a six-week suspension from the Tribunal.

While playing for the Melbourne Football Club, Bugg co-founded ZOOZ Group a social media technology company. In less than 12 months of operations ZOOZ Group grew to a multi-million dollar business leading to Bugg’s retirement from professional sport to pursue his business goals. In 2019, less than a year after retiring from football, ZOOZ Group was awarded the Deloitte Technology Fast 50 Australia Rising Star Award.