The former Chelsea defender has been discussing the 27-year-old striker.
And Bridge is quoted as saying by the Mirror: "Costa is a passionate and aggressive player - that's his edge.
"But he's got to knuckle down. He was stupid to get involved with Mourinho the other week because there will only be one winner.
"He's still a top player and I think Mourinho will get him back to his best."
Costa was criticised for another mini confrontation against Leicester City, when he seemed to suggest the Chelsea defenders were asleep.
Condemning them is fine - unless it's hypocrisy. And, with Costa, it very much is. The Spaniard is way off form and is in no position to criticise anyone.
Is Bridge right, though, in backing the 27-year-old to come good at Stamford Bridge this season? There is certainly a case to suggest Mourinho should opt instead for Loic Remy, or play him alongside Costa as he did in the second half against Leicester.
Sticking with the Spaniard looks as though it could do more trouble than good at the moment.