Captain Sameer Manjrekar was left agonising his soft dismissal after darkness fell on Bardsey’s survival bid.
Bardsey needed to beat relegated Calverley and hope Bolton Villas lost on the season climax to survive relegation to Aire-Wharfe Division Three.
Needing 11 runs from two overs and Villas defeated, Manjrekar’s men looked well set to pull it off.
But two quick wickets, including Manjrekar (27), left them just eight runs short of overhauling Calverley’s 202-9.
Manjrekar said: “It was disappointing especially because it was so close yet so far.
“I thought we had it in the bag.”
Overseas star Umer Yaqoob had hit 65 and taken 3-54 while Pete Pratt’s 41 set up the chase.
Manjrekar added: “We have learned a lot from the season.
“It is a new team and we have come together as a unit. Unfortunately that came too late.”
In Division One, Collingham ended their season with a whimper, losing by 54 runs at home to Bilton.
Toby Jacklin took 5-40 to dismiss Bilton for 120. But the hosts collapsed to 66 all out in their chase.