This is one of those that RAW isn't super clear because Shove is only defined as a "special melee attack", so you can say you push someone with the "stick" of your polearm (like a hockey cross-check), and that should technically qualify.
The Polearm Master bonus action attack triggers on "attack with only a glaive, halberd, quarterstaff, or spear" - those weapon key words implying that the bonus action is allowed when a subset of melee weapon attacks is used.
Eh, I'd still allow it in my games. Even if we listen to Jeremy Crawford that shoving isn't a "melee weapon attack", Polearm Master doesn't use that exact phrasing. Also Shove (in 5e raw) is pretty weak, so I'm against things that nerf it further.
In BG3, this is kind of irrelevant since shove is a bonus action. With polearm master and sentinel, you could totally do this strategy of shove and then prevent the enemy from reaching you. As people above have said, you're sacrificing ASIs for feats. However, in BG3 disengage is also a bonus action. So you could just disengage instead of shoving the enemy away, which is guaranteed to succeed.