Bowyer is back available for Saturday's home clash with Stoke after completing a three game ban for his sending-off against Preston at the tail-end of last season at St Andrews.
The former England player had already been booked when he was involved in a bust-up with Lee Williamson and was given his marching orders after tugging at his shirt.
McLeish is glad to have the experienced Bowyer available but is stressing to all his squad not to pick up avoidable cautions which may cost them crucial bans.
The former Scotland boss said: "It is crucial not to pick up stupid suspensions. You see players taking their shirt off when they have already had a booking and then they are sent to the dressing room.
"It is, for me, a ridiculous rule but the players have got to forget about pulling the shirt off if they score and waving it to the crowd because it is an automatic booking.
"These bookings accumulate and you end up looking back saying 'if I didn't get that booking, I wouldn't have missed this crucial game.'
"So it costs the club and the players themselves. For silly bookings, there is disciplinary action and we have got to remind them of these things that are automatic bookings.
"Things like if the ref blows his whistle and you run on and put the ball in the net or kick it away, pulling jerseys when players are running around from you are automatic bookings.
"Silly bookings have got to be cut out. For example, we don't want to lose Lee like the end of last season when he was getting pulled at first and ends up in a scrap.
"He has got to walk away from that and make sure his reputation is seen as a more mature player, that we well believe he is."
Bowyer, signed on a free transfer from West Ham in the summer after a successful loan spell at Blues, has to wait and see if he will earn an instant recall.
McLeish said: "He might not get a game. The players have done well. When you go out through suspension and the other players have done well, then sometimes it is hard to get back.
"There is no doubt we welcome Lee back to the squad and we will make a decision on whether he starts or not."
Birmingham 11/8, Stoke 2/1, Draw 9/4