Bamford scored his seventh goal for Derby and his 24th of the season (17 for MK Dons) after setting up the opener for Johnny Russell which put Derby on course for the victory that makes them strong favourites for the play-offs.
The 20-year-old had scored in the first minute at Ipswich in midweek and he set Derby on their way again when he supplied the pass across the Charlton box to Russell, who was given too much time and space to turn and beat Ben Hamer with a low drive from 12 yards.
A mistake by Charlton skipper Johnnie Jackson in the 38th minute was seized on by Bamford who squeezed a low shot past Hamer but Derby's first half dominance came under attack in the second half.
Lee Grant had already made one important save before Derby scored and he preserved his team's two goal lead with another diving save to turn aside a shot from the edge of the box by substitute Callum Harriott.
Grant also denied Joe Piggott but Derby finally finished the game as a contest in the 84th minute when Craig Bryson's corner to the near post was glanced in by Chris Martin for his 19th of the season.
McClaren knows how important Bamford has been since his arrival on loan in January and he said: "He came as a striker, that's where he wanted to play but we have kind of played him as one of the three strikers on the right hand side and given him the licence to roam and get in the box and score goals.
"But what has impressed me is his actual work rate, his discipline and the work he does for the teams. It's like we always say to him, his feedback is about if he was at Chelsea, not here, so we demand a lot from him and at the moment, he's delivering.
"I was pleased that the front three scored and we've got back to scoring goals, that's nine in a week and we've had two clean sheets as well. There's a good balance to the team which has shown its mettle and quality and shown it's ready for the run-in.
"We've got to keep this momentum going now and keep doing what we are doing."
Charlton head coach Jose Riga said: "We were not in the game at all in the first half and we had many difficulties. We were not able to play as we can and also we made some defensive mistakes but in the second half we created chances but we must be more efficient at good moments in the game.
"But the main thing is still to believe because I believe for sure that we can avoid relegation. It will not be an easy story but the players have to believe in it as well because we have put something in place.
"The important thing now is that we have a good recovery before we play Leeds on Tuesday. But I do believe and I want to be able, with the players, to write the last chapter in the way that we hope it will be."