I am wondering if I can apply Martial Arts Modified Weapon Damage
You can roll a d4 in place of the normal damage of your unarmed strike or monk weapon. This die changes as you gain monk levels, as shown in the Martial Arts column of the Monk table.
To the Bonus action of Polearm master if I am using a quarterstaff instead of dealing d4?
When you take the Attack action and attack with only a glaive, halberd, or quarterstaff, you can use a bonus action to make a melee attack with the opposite end of the weapon. The weapon's damage die for this attack is a d4, and the attack deals bludgeoning damage.