The 35-year old Dutch midfielder is currently a free agent and training with the Hoops after his contract at the Stadium of Light finished at the end of last season.
Celtic boss Neil Lennon is running the rule of the former Barcelona, Chelsea and Liverpool man and his old Black Cats mate Bardsley, a Scotland international, is confident he would do well at Parkhead.
"I've no doubts this would work out for Celtic," he said.
"I'm surprised he hasn't got a club. He's still a great player and we were disappointed not to keep him at Sunderland.
"If he goes to Celtic he'll be a great success. I'm surprised he hasn't got himself a Premiership club because even though he's 35 he's still fit and looks after himself.
"The way he plays the game is clever. The football flows through him and has a lovely left foot. I'm sure Neil Lennon knows what he's all about.
"He's had a tough time but I'm sure if he gets all his players fit and brings in experience like Bolo's it won't be long in coming."