The Bees had not been able to play for a number of weeks due to the bad weather and were eager to get going again.
But they had to be patient for just a little longer than expected as the Cleckheaton players arrived late for the Division Four fixture due to heavy traffic.
When the match finally started Bingley made a great start cheered on by a sizeable home crowd.
A well-rehearsed penalty corner routine saw an accurate pass out from Janice Reid to Jane Sharkey, who slipped the ball to Becky Tatham and she fired into the corner.
Bees keeper Rachel Fuller made some great stops during a player of the match display but could not prevent Cleckheaton equalising just before the interval.
Bingley regained the lead when Lucy Walsh gave a great pass to Janice Reid and she set up Sian Porter to score from a difficult angle.
But they were denied victory when the third-placed visitors beat Fuller again towards the end of the contest.
Meanwhile, the Bees first team slumped to an 8-0 defeat at title-chasing Boston Spa & Acomb to dent their hopes of avoiding Premier Division relegation.