Having wasted one of their games in hand by losing to fellow strugglers Barnsley in midweek, the Addicks once again missed a host of opportunities to sink a Wanderers side with little to play for in mid-table.
They are now two points above the danger line but know a win for Millwall at Middlesbrough on Saturday will see their south London rivals climb above them.
A lack of goals has been the problem all season and yet again they created plenty of chances, only for their finishing to let them down.
Bolton, whose fine late-season run of one defeat in 12 has steered them well clear of trouble, almost took an early lead when Liam Trotter's volley was kept out by Ben Hamer.
But after that it was virtually all Charlton, with Astrit Ajdarevic firing their first opportunity wide from Jordan Cousins' knock-back.
Ajdarevic then sent Reza Ghoochannejhad through but Bolton keeper Adam Bogdan raced out to block at the Iran striker's feet.
Simon Church fluffed a header from Cousins' cross and Ajdarevic, Ghoochannejhad and Johnnie Jackson all took aim with miserably familiar results before the interval.
The hosts could have gone in at half-time behind had David Wheater kept his volley down, while shortly after the break Diego Poyet cleared Matt Mills' header off the line.
But Charlton continued to pile forward and just before the hour mark they felt, with some justification, that they should have had a penalty when Bogdan sent Church sprawling in the area, but referee Brendan Malone thought otherwise.
Then came their first shot on target, in the 63rd minute, with Bogdan untroubled by Ghoochannejhad's weak effort from outside the area.
Moments later Church should have given Charlton the lead when he met Cousins' low cross six yards out but the striker scuffed his shot straight at Bogdan.
Still the chances came and went, Bogdan holding Ajdarevic's curler, Cousins skewing a shot the wrong side of the post, Jon Obika off target with a header and Michael Morrison nodding wide from Jackson's corner.
In the end Charlton were grateful for a point, however, after Neil Danns wriggled clear in front of goal only to scoop his shot over the crossbar from 12 yards.