Bell-Drummond was born in Lewisham in south-east London in 1993. His parents are of Jamaican descent and he has described how watching both West Indian and English cricket home was a major influence on his development. He was spotted by Kent County Cricket Club playing for Catford Wanderers as a seven-year-old and progressed through the county system, scoring his first century for the under-10 side aged just seven. He played for Kent age group teams, scoring centuries at every level, before joining the Cricket Academy at Kent where he was awarded the John Aitken Gary Trophy as the Academy Scholar of the Year in 2010. He signed a three-year professional contract with Kent in September 2010 at age 17.
Bell-Drummond won a scholarship to Millfield School and played cricket for the school team as well as for England at under–15, under–17 and under–19 levels, captaining the under–17 side against Sri Lanka in 2010. He completed his sixth form studies at the school in 2012 after signing his professional contract with Kent and was named the Young Wisden Schools Cricketer of the Year in the 2012 edition of Wisden after scoring over 800 runs for Millfield in 2011.
Having represented England and under-15 and under-17 levels, Bell-Drummond played for the England under-19 cricket team against Sri Lanka in 2010. He made his youth Test debut on 21 July 2010 at the County Ground, Northampton before scoring unbeaten 88 in the second youth Test later in the same month, aged only 16. He played in both under-19 Test matches and in four youth one-day international matches during England's return tour of Sri Lanka in January and February 2011.
In July 2011 Bell-Drummond played in a one-day series against South Africa under-19s. He top-scored for England in three of the seven matches in the series and was the leading run scorer for the team in the series, scoring 329 runs in seven innings at an average of 47.00.
After touring Bangladesh with the England under-19 side during January and February 2012 and again leading the team in run scoring, playing in all seven youth ODIs, Bell-Drummond played in a four-way 50-over competition against the Australia, India and New Zealand under-19s in North Queensland in April 2012. He was the leading run-scorer in the competition with 287 runs at an average of 95.66, including a match-winning 103 not out against Australia in an innings when the next highest score for the England team was 28. Later the same month he was described as "perhaps the most exciting young batsman in the country" and was named in the England team for the 2012 Under-19 World Cup, held in Queensland in August 2012. By his standards he had a disappointing tournament after being tipped as "one of the batsmen to watch".
Bell-Drummond made his first-class cricket debut for Kent at the age of 17 in a University match against Loughborough MCCU in May 2011, scoring 80 runs from 103 balls. In July the same year he made his senior List A cricket debut in a Clydesdale Bank 40 match against Worcestershire before going on to play in three County Championship matches for Kent towards the end of the 2011 season. He spent most of the 2012 season playing for Kent's Second XI, making only two first-class appearances during the season, including against the touring South Africans at Canterbury
He made his maiden first class century in April 2013 against a Cardiff University side and used the innings to become a regular in the Kent side during the 2013 season. After cementing his place in the Kent side in all forms of cricket and scoring a century against the touring Australian side in June 2015, Bell-Drummond was awarded his county cap in August 2015. In August 2015 he deputised as an emergency wicket-keeper in Kent's County Championship match at Derby when Sam Billings suffered a finger injury, keeping wicket until Ryan Davies arrived from Second XI duty to act as a substitute. He deputised again in May 2017 when Adam Rouse injured a thumb, taking one catch behind the stumps.
In December 2015 Bell-Drummond made his first appearance for England Lions against the United Arab Emirates in a T20 match in Dubai. He scored 5 runs from 5 deliveries opening the batting. Later the same month he played in the final game of the five match T20 series against Pakistan A scoring 17 runs.
Bell-Drummond made an excellent start to the 2016 domestic season, hitting his maiden first-class double-hundred against Loughborough MCCU followed by a century in his first innings of the County Championship season against Leicestershire. He and Tom Latham then combined for two first-wicket century partnerships in Kent's opening home match of the Championship against Glamorgan, only the third time this had been achieved in the same Championship match in the County's history. Bell-Drummond was selected for England Lions again during the 2016 summer, playing limited overs matches against both Pakistan A and Sri Lanka A. He scored his highest List A cricket score of 171 not out against Sri Lanka A at Canterbury during the series of matches as he combined with Ben Duckett to post the second highest List A partnership on record.
During the 2016–17 English off-season Bell-Drummond was again selected for the Lions, playing against the UAE in Dubai during December and in the List A matches against Sri Lanka A in March, scoring a century in the 4th match of the series. He was also chosen to play in the North v South pre-season series in the United Arab Emirates.
as of 26 July 2016