Bridges’ stubborn defence and heroic goalkeeper Kieron Thorp combined to earn a tough away draw.
Bridges’ Mitch Casselman and Allan Tait had efforts blocked in quick succession.
Jamie Byatt had a volley blocked at the other end and a good run by Roscoe DSane ended with him firing over.
But after 11 minutes a long ball found the tireless Byatt, whose angled shot gave Leafe the lead.
Four minutes later Tait nodded the ball down for Jamie Crellin to volley home superbly.
Thorp made a string of saves to deny Sam Clayton, Vernon Francis, Clayton and Ryan Fowler.
Casselman fired over after Tait had laid the perfect ball back to him from a John Lansdale throw-in.
Thorp was beaten as Fowler rattled the crossbar and then the normally reliable Byatt contrived to mis-kick from less than a yard out.
The visiting defence showed their resilience and stamina with Matt Daniel and the ever-reliable Crellin both made goalline clearances.
Bridges might have even snatched an unlikely winner as Tait’s under-hit stab was just about cleared off the line, whilst virtually the last action saw Hakeem Adelakun’s brilliant crossfield ball laid back by Tait to Dan Mobsby, whose great effort was somehow deflected to safety.
Bridges: Thorp, Cooney, Daniel, Sargent, Brake (Mobsby 77), Crellin, Touray (Adekakun 70), Lansdale, Tait, Casselman, Whitehead (Godfrey 65).
Unused sub: Pulling
Aerotron Man of the Match: