The Republic of Ireland international left the Stadium of Light at the end of last month and joined the Championship club on a loan deal until the end of the season.
McGeady had been frozen out at Sunderland, Phil Parkinson making it clear he had no future at the Stadium of Light while he remained manager of the club.
The 33-year-old made his debut for Charlton as a second-half substitute against Nottingham Forest and Bowyer was happy with his new player's initial output.
"Aidy did very well," Bowyer is quoted by The Herald as saying. "That's what I want, competition for places. It'll make my job harder, but it makes our team better.
"I want to play Aidy, I want to give him a chance. I see him in training and he's very good."
He is out of contract at the Stadium of Light at the end of the season and, with no future on Wearside under Parkinson, he is very much playing for his future at the moment.
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