Bashir was struck for 38 in an over on the second day of Worcestershire's match at home to reigning First Division champions Surrey.
Fellow England international Dan Lawrence did the bulk of the damage with five successive sixes.
Lawrence cleared the boundary with the first five balls of the over in an arc between long off and wide long on at New Road.
The next ball from the 20-year-old Bashir, on loan to Worcestershire from Somerset, went for five wides.
Lawrence took a single off a no-ball before Dan Worrall failed to score off the eighth delivery from Bashir, who only made his Test debut during England's tour of India earlier this year.
The total equalled the 38 in an over struck by Andrew Flintoff off Alex Tudor for Lancashire against Surrey in a Championship match at Old Trafford in 1998.
Lawrence went on to make a career-best 175 in a Surrey first-innings total of 490 and then took two wickets as Worcestershire slumped to 147-7.
West Indies great Garry Sobers, playing for Nottinghamshire, became the first batsman to hit six sixes in an over of first-class cricket off Glamorgan's Malcolm Nash back in 1968.
But all of Nash's deliveries were legal, with 36 the maximum number of runs that can be scored in an over without wides or no-balls.
