Bennett joined the youth-team at Oldham Athletic at the age of ten, and left Boundary Park five years later. He went on to make his debut in the Manchester League for Springhead at the age of 16. He moved on to Curzon Ashton the next year, before being signed to Northern Premier League Division One North side Mossley in November 2013. He scored eight goals in 22 games during the second half of the 2013–14 season. He signed with Northwich Victoria, where he was christened "Richie" by manager Jim Gannon, having previously only been known as Richard or Rich. He scored 44 goals in two seasons with the "Vics" and helped them to win the 2014 Cheshire Senior Cup. During his time playing as an amateur and semi-professional he worked in customer sales for Marks & Spencer, in a call centre and also a spell as a care assistant working with dementia sufferers. He also became a father at the age of 17.
Barrow
On 17 May 2016, Bennett signed a two-year contract at National League club Barrow. It was reported that he opted to go to Holker Street ahead of competition from League Two clubs. He went on to score 22 goals in 53 games as Paul Cox's "Bluebirds" finished the 2016–17 season in seventh-position, just missing out on the play-offs.
Carlisle United
On 25 July 2017, 26-year old Bennett signed for Football League side Carlisle United for an undisclosed fee on a two-year contract. Bennett stated that "I think I'm ready for the step up... I've still got a lot to prove, a lot to learn but I'm more than willing to get my head down and do it." On 30 September, he was one of three players sent off in a 1–0 defeat at Crawley Town; he was shown a straight red card for elbowing defender Josh Yorwerth. It took him 15 games before he scored for the "Cumbrians", but credited the support of his teammates and manager Keith Curle in helping him to break his scoring duck. His first goal for the club came on 28 October, in a 2–2 draw at Chesterfield. On 4 November, he scored a brace in a 3–2 FA Cup victory over former club Oldham. He ended the 2017–18 season with eight goals in 47 appearances. Having been limited to 13 league starts by new manager John Sheridan, Bennett signed for Morecambe on loan for the rest of the 2018–19 season on 17 January 2019; "Shrimps" boss Jim Bentley admitted he had been monitoring the player for some years. David Holdsworth, director of football at the "Blues", said that Carlisle would monitor his progress and still retained the option of extending his contract at Brunton Parkin the summer. He scored five goals in 16 games at the Globe Arena, however was not retained at the end of the season by new Carlisle manager Steven Pressley.
Port Vale
On 21 June 2019, Bennett signed a two-year contract with League Two side Port Vale. Manager John Askey said that he hoped having Bennett available to him would take pressure off star striker Tom Pope. He scored his first goal for the "Valiants" on 17 August, three minutes after coming on for Pope in a 1–1 draw at Salford City. Three days later he was given his first start for the club and this time scored after four minutes in what ended as a 2–1 victory over Forest Green Rovers at Vale Park. He lost his first-team spot in late-November to Pope and then Mark Cullen, before scoring a brace in a 3–1 home win over Exeter City on 28 January in what was his second league start in two months; despite this achievement Bennett admitted that "it probably wasn't my best performance. I have a lot to improve, I know that myself". He left the club mid-way through the 2019–20 season after scoring seven goals from 30 games.
Stockport County
On 12 March 2020, Bennett signed a two-and-a-half year contract with Stockport County after being sold for an undisclosed fee, who were just outside the National League play-offs under former Northwich manager Jim Gannon.
Style of play
Standing at, Bennett is a hard-working forward who is good in the air. Describing his own game, he said that "I would like to say I'm aggressive, quick - one of them annoying strikers that doesn't really give you time to think about what you are doing on the ball".
