The Town racked up a host of chances in both halves, with Matty Pearson and James Colllins both denied a hat-trick apiece in the opening 45 minutes with Moncur going even closer on the stroke of half-time, rattling the crossbar from the edge of the box.
The former Barnsley man made the breakthrough four minutes into a second half in which manager Graeme Jones had made seven changes, with an eighth to follow with teenager Sam Beckwith coming on for Moncur midway through.
It was from the youth team midfielder's through ball that Jervis rounded Bedford's impressive goalkeeper Alex Bennion, who had pulled off a string of excellent saves, to net the Town's second goal with five minutes remaining.
The Eagles halved the deficit two minutes later with a neat finish from striker Tre Mitford, but the Town had done enough to ensure another win.
FIRST HALF HATTERS: Shea, Neufville, Pearson, Jones, Panter, Cranie (c), Shinnie, Mpanzu, Moncur, McManaman, Collins.
SECOND HALF HATTERS: Stech, Neufville, Pearson, Jones, Galloway, Berry, Tunnicliffe, Moncur (Beckwith 67), Lee (c), Jervis, Cornick.
GOALS: Moncur 49, Jervis 85
ATT: 1,604