Bolus was born in Whitkirk, Leeds, Yorkshire. He learned his cricket with Whitkirk before moving to Leeds in 1953, and then to Bradford. In his debut List A cricket match, he scored 100 not out in his team's total of only 159, the lowest all-out total to include a century in List A cricket's history.
He began his first-class career in his native Yorkshire in 1956, playing for seven years. His first-class debut was Yorkshire versus M.C.C., at Lords, in 1956. He played 107 matches for Yorkshire, with a highest score of 146 not out against Hampshire at Portsmouth in 1960. His best bowling figures were 4 for 40 against Pakistan at Park Avenue in 1962.
He moved on to Nottinghamshire in 1963, after Yorkshire opted for a relative unknown, Geoffrey Boycott, who was six years younger. For Nottinghamshire he played 269 matches, with a highest score of 202 not out against Glamorgan at Trent Bridge in 1963, and best bowling figures of 2 for 24 against the West Indies, also at Trent Bridge in 1966. He was made county captain in 1972.
Bolus became the third player to be capped by three counties, and the first to captain two different county sides in successive seasons, when he moved to Derbyshire in 1973. He played 64 matches for Derbyshire, with a highest score of 151 against Oxford University at the Bass Worthington Ground in Burton upon Trent in 1975.
He twice scored more than one thousand runs in a season whilst playing for Yorkshire, as well as ten times for Nottinghamshire and twice for Derbyshire.
A solid county performer, particularly strong off his pads, his Test batting average of 41.33 is higher than his overall first-class average of 36.91. He was unlucky not to play more Tests, particularly after a strong tour of India in 1963/64. He hit the first ball he faced in Test cricket, bowled by Wes Hall, back over the bowler's head for four. He was unable to convert any of his four Test fifties to three figures, and found himself overtaken in the international reckoning by Geoff Boycott and John Edrich. Bolus does hold two unusual Test match records - the most Tests in a complete career without ever recording a single figure score (seven), and the most Test Match innings in a complete career without ever recording a single figure score (twelve).
He effectively retired in 1975 with over 25,500 first-class runs to his name. He appeared twice in the B and H cup at the start of the 1976 season. He became an England Test selector in the 1990s. After his first-class career he took an appointment with Gedling Council in Nottingham in 1976, while also playing for Bradford. Later he played for Cleckheaton, Brighouse and Farsley, leading the team to a Priestley Cup win in 1983. He is an Honorary Life Member of Whitkirk Cricket Club.
He is one of the small band of captains to send off one of his own players, dismissing the Derbyshire and England paceman, Alan Ward, from the Queen's Park, Chesterfield, ground after Ward had declined to resume bowling.
In his later after dinner speech career, Bolus opened with the line, "For those of you who saw me bat... let me apologise".
He is married to Gloria, has two sons and one daughter, and now lives in Nottingham.