Bowyer retaliated after being on the receiving end of a challenge from Baggies defender Gonzalo Jara and reacted with a lunge at Gabriel Tamas which resulted in him picking up a yellow card.
McLeish instantly substituted Bowyer, who was then involved in a verbal exchange with a female fan situated behind the City dugout.
McLeish said: "I just didn't want to take a chance. Lee is mature but I didn't want to take a chance and get egg on my face.
"We were talking about taking Alexander Hleb off at that time because he has not played a lot of football and he looked fatigued.
"Then Bowyer got the booking and I took him off just in case. He is more mature now and he maybe would have seen it through but I didn't want to take any chances."
As regards the Bowyer-fan confrontation, McLeish said: "Someone lambasted Lee when he came off and I saw 'Bow' trying to pacify them.
"That's the only thing I can tell you about it. I know some people were having a go from the seats behind the dugout. When I turned around 'Bow' was telling them to calm down.
"It is difficult when you are coming off the pitch, have been booked, been taken off when you don't want to come off, and someone is lambasting you from the terracing."