Chris Dennison (42) helped give the Scholes innings a good start as he shared a 69-run stand with Shoukat Ali.
A further 110 runs were added for the second wicket between Ali and Sam Gatenby (68).
Ali struck 79, including eight fours and three sixes, and the total was given a further boost by Aditya Waghmode (37) as they posted 256-8.
Ed Brown was pick of the Bingley bowlers with 5-43 and then made 103 not out and was joined in an unbroken last-wicket stand of 92 by Jonathan Wilmshurst (9no).
Bingley had been reduced to 127-9 as Yasir Ali (5-42) led the way before Barber unleashed a barrage of lusty blows as he struck nine fours and seven sixes as they closed on 219-9.
New Farnley bounced back from defeat at Cleckheaton the previous week as they defeated Woodlands by nine wickets.
Woodlands were left to rue their decision to bat first as paceman Andrew Brewster claimed 4-25 and had them in trouble at 68-9 before a last-wicket stand of 55 between Muhammad Bilal (32no) and Kez Ahmed (21) helped them to 123.
Steve Bullen hit an unbeaten 61, while fellow opener Simon Lambert made 37, as Farnley cruised to victory.
Bottom-team East Bierley gave defending champions Hanging Heaton a huge scare before losing by four wickets.
Half-centuries from Awaise Hussain (53), Danish Hussain (52) and Shabbir Rashid (50no) helped East Bierley to 240-6.
Paceman Tom Chippendale (4-61) was again the best of the Hanging Heaton bowlers.
Heaton were quickly reduced to 36-4 before opener Nick Connolly (80) and James Keen (47) added 115 for the fifth wicket.
Both fell in quick succession and East Bierley sensed a second win of the season.
Those hopes were extinguished by big-hitting David Stiff.
He made an unbeaten 62 from just 44 balls, hitting five sixes and four fours, to see his side home and Hanging Heaton lie fourth in the table.