Notts dominated the first half, with shots from Craig Westcarr and Alan Gow forcing Rob Elliot into diving saves first to his left and then his right.
Joe Anyinsah then nodded down to Bradley Wright-Phillips, but his effort was covered by Stuart Nelson.
Gow's run and shot stung Elliot's palms in an open but goalless end to the half.
The hosts grabbed a deserved lead four minutes into the second period though, as Gow's low free-kick was turned in from close range by Bishop.
A half-volley by Scott Wagstaff was then saved by Nelson, while Westcarr blazed over and Karl Hawley failed to capitalise on Elliot's hesitancy.
In the 63rd minute, Mike Edwards fouled Anyinsah in the box, but Wright-Phillips' low penalty was saved by Nelson.
On the final whistle, Lee Hughes chested a ball into the path of Westcarr, whose stinging volley was well saved.
Notts County 1-0 Charlton: Match Report - view commentary, squad, and statictics of the game as it happened.