Nicknamed "The Bullet", Bunting formerly competed in British Darts Organisation (BDO) events, where he was a two-time World Masters champion.

He reached his first major semi-final at that year's World Grand Prix, and has since won three ranking titles on the PDC Pro Tour.

In July 2008 he reached the quarter-finals of the BDO British Classic where he lost to Scotland's Ross Montgomery live on Setanta.

The following year, Bunting once again qualified and won his first round match 3–0, this time against Brian Woods with the tournament's highest three-dart average of 94.62.

In the last 32 Bunting played another Lancashire county teammate and newly crowned Romanian Open Champion Joe Murnan.

In October 2012, Bunting took his largest career title by winning the Winmau World Masters as the number one seed, defeating Tony O'Shea 7–4 in the final.

In July, Bunting won the England Masters title at the Pontins Southport beating Paul Jennings in the final 6–5.

Bunting successfully retained the World Masters title in 2013, becoming only the fourth man to do so after Eric Bristow, Bob Anderson, and Martin Adams.

[5] At the Zuiderduin Masters, Bunting reached the final for the second straight year but this time was comprehensively beaten by Wilson, 5–1 in sets.

[8] Bunting's first tournaments were the UK Open Qualifiers and he won the second and £10,000 by beating eight players, concluding with a 6–5 victory over Andrew Gilding.

[9] The result saw him enter the 2014 UK Open at the third round stage where he made his PDC televised debut against Kevin Dowling.

[11] He made his European Tour debut at the 2014 German Darts Masters and won through to the semi-finals where he lost to Phil Taylor 6—3.

[12] Bunting's second PDC final came at Players Championship 10, in a run which included a victory over world number one Michael van Gerwen, before being defeated by Terry Jenkins 6–3.

[16] In October, Bunting reached the semi-finals of the World Grand Prix by beating Ronnie Baxter, Wright and Richie Burnett.

[18] Bunting produced a superb performance in the second round of the European Championship as he averaged 102.21 in beating Taylor 10–9 having never been behind during the match and missed a double 12 for a nine-dart finish.

[20] Bunting reached the quarter-finals for the third major event in a row by beating Wade 10–8 at the Grand Slam of Darts, but lost 16–9 against Mervyn King.

[22] In his debut at the 2015 PDC World Darts Championship, Bunting saw off Robert Marijanović 3–1 in his first match, before defeating James Wade 4–1.

Bunting could not win a leg in the deciding set to be defeated 5–4 and end his chances of becoming the first player to hold both versions of the World Championship at the same time.

[25] After Van Barneveld stated that his opponent's performance had shown he was a world class player, Bunting was left in tears on stage in the post-match interview.

[26] Following the World Championship final, Bunting was named as a Sky Sports Wildcard to compete in the 2015 Premier League Darts.

[34] Bunting did reach the quarter-finals of the inaugural World Series of Darts Finals, but was heavily beaten by Phil Taylor 10–3.

[35] Bunting met Raymond van Barneveld at the World Championship for the second successive year, this time in the second round.

[37] En route to the final of the second Players Championship event, Bunting overturned a 5–0 deficit against Adrian Lewis to win 6–5.

[38] Despite averaging 102.48, he was only ahead of Mensur Suljović in the first leg of their opening round World Matchplay match as he lost 10–8.

[40] He was knocked out in the second round of both the World Grand Prix and European Championship, 3–0 in sets by Kim Huybrechts and 10–4 by Jelle Klaasen respectively.

[41] Bunting missed seven darts for the match in his first round tie with Darren Webster at the 2017 World Championship and bowed out 3–2 in sets.

[44] Bunting began 2021 on a high by reaching the semi-finals of the 2021 World Championship beating Andy Boulton, James Wade, Ryan Searle and Krzysztof Ratajski on the way, before being eliminated by the eventual champion, Gerwyn Price.

[45] Bunting later reached the semi-finals of the 2021 World Grand Prix, following victories over Daryl Gurney, Wade and Searle.

[50] At the 2024 UK Open, Bunting achieved victories over Danny Lauby Jr., Kevin Doets and Peter Wright to reach the quarter-finals, where he was defeated 10–2 by world number one Luke Humphries.

At the 2025 World Championship, Bunting defeated Kai Gotthardt and Madars Razma before whitewashing Luke Woodhouse 4–0 to reach the quarter-finals.