A Sheffield schoolteacher, Bate spent his early playing career with Alfreton Town before joining Boston United in 1971, debuting in the 3-1 Northern Premier League home victory over South Liverpool on 14 August 1971. It was with the Pilgrims that he began a long association with Howard Wilkinson, captaining the club under Wilkinson's management whilst also securing his UEFA "A" Licence in 1973. His final game for the club echoed his first: a 3-0 Northern Premier League home victory over South Liverpool on 6 December 1975 before Bate moved to Buxton as player-manager.
Wilkinson moved to Mossley in December 1976 as player-manager and when he resigned the following May he recommended Bate as his successor and Bate was duly appointed player-manager in June 1977. However, despite steering Mossley into the first round of the FA Cup for only the (then) third time in their history, he departed the club following a 2-2 draw with Frickley Athletic on 2 January 1978.
Bate joined Sheffield United as a youth team coach in 1978 before succeeding his mentor Howard Wilkinson as Football Association North West Regional FA, Staff Coach in 1980, a post he held until 1985 when he joined Notts County as chief coach.
In June 1987, Bate was appointed manager of Southend United by the club's chairman Vic Jobson without consulting his fellow board members. He reign lasted just ten games with a solitary victory in the Football League Cup and he departed with the worst record of any Southend manager in history.
Bate moved on to join Lincoln City as assistant manager to Colin Murphy, helping the club regain its Football League status at the end of the 1987-88 season. He moved on to rejoin Wilkinson at Leeds United acting as a coach between 1988 and 1992. He moved to Malaysia as Technical Director, a role he held from 1992-1995, before joining the coaching staff of Hereford United. In 1998 he became the coach of the England youth set-up working with the U16, U17, U18, U19 and U20 teams.
In September 2005, the appointment of Bate as the Canadian Soccer Association's Technical Director was announced with the role commencing on 14 October 2005. He held the role for ten months before resigning in order to join Watford.
In July 2006, Bate was appointed Technical Director at Watford with the Hornet's then manager Aidy Boothroyd being quoted as saying "I want Watford Football Club to have the best Academy in the world and I believe we have captured the best developer of talent in the world in the shape of Richard."