Chances were few and far between in an even first half, with Davies blasting one effort high and wide and James Pritchard firing a free kick over the bar after John Gray was hacked down 25 yards out.
Jamie Jackson had to be alert to push a header away, with the rebound put wide by Tom Clarke.
Sloughâ€™s best effort came from the head of Steve Daly, whose effort from Daviesâ€™ corner was saved brilliantly by Manley, away for another corner. Daly got on the end of this cross too, only to see his header hit Lee Riddellâ€™s legs and cleared away to safety.
Bridgwater gradually stamped their authority on the match, forcing Slough to resort to long balls and clearances, without creating anything clear-cut.
Pritchard headed a Terry Davies cross wide at the near post for the visitors, and Gray saw a first-time volley touched wide as neither side could register a goal before the half-time whistle.
Jackson was required to make a smart save very early into the second half as Bridgwater looked to gain the advantage immediately.
A good chance for the hosts arrived when the otherwise impressive Ryan Wharton, making his debut, made a mistake which let in Mike Mackay, but the striker put the ball just wide.
The game evolved into quite a scrappy affair, with much of the play in the air and neither side keeping possession for extended spells.
Another good chance fell to Bridgwaterâ€™s Tom Clarke, but last-ditch defending from the Slough rearguard snuffed out the chance.
In the final twenty minutes or so, the hosts raised their game as they searched for a vital goal, and forced a lot of pressure.
However, Slough had a great opportunity to gain the advantage when Usif Bangura, who had only just replaced Davies, was hauled back by Bridgwater substitute Steve Orchard on the end of the box. Orchard, as last man, was dismissed.
Unfortunately from a Slough perspective, Pritchard fired the free kick straight at Manley, who saved comfortably.
In a frantic finish, Laurence Brown fired over the bar before Ryan King had a fantastic chance to snatch the winner for Bridgwater, but Jamie Jackson came to the rescue with a save to ensure Slough took another vital point ahead of the final game at Fleet.
Bridgwater Town Line up
1. Tom Manley, 2. Jamie Price, 3. Jamie Laird, 4. Pete Monks, 5. Jak Martin, 6. Brett Trowbridge, 7. Ben Kirk (c), 8. Dan Forward, 9. Mike Mackay, 10. Tom Clarke, 11. Nat Pepperell. Subs: 12. Chris Young, 14. Steve Orchard, 15. Ryan King, 16. Craig Laird, 17. Richard Lamcraft.