David Lucas, who was back from injury was the only chance to the team which draw 2-2 last week at Southend.
Gordon Greer had Swindon's best chance of the first half hitting the bar from a header.
Swindon finally took the lead on 65 minutes with a goal from Kevin Amankwaah aftetr a Ward corner.
Deep into injury time Charlton grapped a late equaliser when Bailey was left unmarked in the box and was able to beat Lucas to make it 1-1.
Overall a good game, which Swindon should have won. This leaves Swindon still in 6th place going into Tuesday night's home game against Oldham.