Gary Setchell’s men came back from being 3-1 down at half time, to level with 15 minutes to go and secure victory with two late goals.
The Division One South champions took the lead after 20 minutes in Saturday’s match, watched by a disappointingly low crowd of 302 at the Eyrie.
The visitors then restored their two-goal cushion just before half time.
It took until 20 minutes into the second half for Craig Mackail-Smith to give Bedford some hope at 2-3 and Hugh Alban-Jones equalised in the 75th minute setting up an exciting last quarter of an hour.
Just four minutes later Rory McAuley made it 4-3 to the hosts and Mackail-Smith made sure of the victory in 90th minute for a final score of 5-3 to the Southern League Division One Central champions.