As mentioned in this question, Shillelagh and Polearm Master Interaction, Shillelagh appears to allow Wisdom-based fighting on the Bonus Action attack, but because Polearm Master specifies a d4 damage die, and because Polearm Master's damage die is the more specific case, it is not overwritten by Shillelagh's d8 damage die.
Therefore, a Shillelagh Polearm Master Bonus Action Attack will be a Wisdom-based attack with 1d4 damage.
However, in the case of Elemental Weapon, which provides a +1 to attack rolls and bonus +1d4 damage of a specific element, does that get applied to your Polearm Master Bonus Action attack?
I'm inclined to say yes, but Jeremy Crawford did not say much on the previous Shillelagh question and I'd be interested to know if there's more information on the topic.
Best Answer
Yes, it does.
The Polearm Master feat (PHB, p. 168) states:
The reason why shillelagh and Polearm Master interfere is because shillelagh also states
However, elemental weapon (PHB, p. 237) simply states that you get a bonus to attack rolls (which PM grants) and deal an extra 1d4 damage when it hits:
Regardless of which end of the weapon hits, the weapon altogether did hit, hence you get both the +1 and the +1d4 bonus damage.