Bates scored her 28th international half-century in a dominant performance against New Zealand's depleted batting line-up.
England's relentless accuracy in the middle overs proved too much for the White Ferns, who could only reach 44-1 after the six-over powerplay. At the same stage, England had reached 41-1.
Georgia Plimmer added 59 runs for the second wicket with Bates. However, she struggled once the spin of Sarah Glenn and Charlie Dean was introduced. She eventually fell to Glenn for 21 runs from 24 balls.
In a promising sign for England without world number one Ecclestone, the spinners bowled beautifully in tandem.
Both were miserly and constantly cramped the batters for room. Glenn finished with figures of 1-17 and Dean with figures of 0-21. Meanwhile, Knight finished with figures of 0-10 from two overs of her part-time off-spin.
Bates was caught by Dunkley off Bell in the 17th over, leaving the hosts at 109-4. Unfortunately, their slim hopes vanished with her departure. Bates played a counter-attacking innings, hitting nine boundaries.
Lauren Filer made her T20 debut and bowled two overs for 22 runs. All-rounder Danielle Gibson finished with figures of 0-33 from her four overs. Coach Jon Lewis is testing young talent ahead of the T20 World Cup in the autumn.