Lyle Taylor’s 19th-minute goal separated the sides as basement boys Bradford remain six points from safety.
It was a chalk-and-cheese performance following last week’s home hammering at the hands of Blackpool and Bowyer said: “I demanded a response and I certainly got it.
“Defensively, we were organised and difficult to beat. If it wasn’t for one lapse in concentration we could have got something.
“We came to frustrate them. They’re a wonderful team and you just have to look a the talent they bought in in January.”
The Addicks could have been home and dry by the break. Taylor beat Richard O’Donnell low to his right but the goalkeeper did well to deny Igor Vetokele and Taylor almost had a second when he struck the post from outside the area.
Jacob Butterfield squandered a glorious chance to level 10 minutes before the break, with Taylor lashing over at the other end.
After the restart, David Ball was kept out by Dillon Phillips before agonisingly hitting the post for the battling Bantams.
Just after the hour, potent threat Taylor fired over and the forward also acrobatically hit over from Tarique Fosu’s cross.
City’s Eoin Doyle was through on goal before Anfernee Dijksteel denied him the chance to shoot.
Charlton Athletic: Phillips, Dijksteel, Bauer, Sarr, Purrington, Cullen, Reeves (Pratley, 79), Aribo, Williams (Fosu-Henry, 61), Vetokele (Pearce, 90), Taylor. Unused substitutes: Maxwell, Solly, Lapslie, Parker.
Bradford City: O’Donnell, Caddis, P O’Connor, A O’Connor, Wood, O’Brien, Akpan (Wright, 80), Ball, Butterfield (Miller, 85), Anderson (Clarke, 85), Doyle. Unused substitutes: Wilson, Chicksen, Knight-Percival, Devine.
Referee: M Coy (Durham).