Pushing attack activates with a weapon attack and Shield master is a bonus action to shove. Can these be combined to a 20' shove or would it have to be 15' shove followed by a 15' move and another 5' shove?
No. You'll have to move to shove again.
Pushing Attack requires a weapon attack:
When you hit a creature with a weapon attack...
A shove is not a weapon attack:
Using the attack action, you can make a special melee attack to shove a creature, either to knock it prone or push it away from you.
As soon as you push the target with Pushing Attack, the creature is moved 15 feet, so you have to get within melee range to shove.