"Any character can shove as a bonus action if they get an attack of opportunity (including the shield master) "A shove is in fact an attack.
Any character can shove as a bonus action if they get an attack of opportunity (including the shield master) So what makes the shield master feat special if he is severely limited to when he can use it?
My argument is that the mention of the "attack action" means that these bonus attacks are PART of the attack action. This is the case for Two weapon fighting, Magic weapon as well as for Polearm master. Since it is part of the attack action then the rule is that it can be done in any order.
The mistake people are making is treating a bonus attack as something separate from the attack action. It uses your bonus action but there are no examples of such attacks taking place "outside" of the attack action. I gave three other examples... Shield master shove is no different...
I have no idea what you are talking about.
There is AFAIK no link between attacks of opportunity (reaction) and bonus action shoves.
Furthermore, shoves and grapples cannot normally be used as Opportunity Attack reactions since they both specifically require the attack action and thus are not available for OA reactions. They could be "Ready" but that's a different thing.
So, unless you just tossed out a chuck of unlabeled house rules - that which you just said made no sense.