The bolded is untrue. Please refer to the shield master debates for clarification.
I'm not sure Shield Master is relevant here. SM does not have a timing specification:
If you take the Attack action on your turn, you can use a bonus action to try to shove a creature within 5 feel of you with your shield.
Bonus actions without timing specifications can be taken at any time during your turn, so you can declare you take the attack action, then use a bonus action to shove before actually making any of your attacks.
On the other hand (

When you take the Attack action and attack with a light melee weapon that you're holding in one hand, you can use a bonus action to attack with a different light melee weapon that you're holding in the other hand.
I tend to agree with others that "When" implies you can't take the bonus action until *after* you make 1 attack as part of the attack action. At the very least that seems to be RAI, based on a related SA compendium question(v2.2 pag 11):
With two-weapon fighting, can I use both attacks (normal and bonus) to shove a creature? No. Two-weapon fighting (PH, 195) doesn’t grant the bonus attack unless the first attack is made with a light melee weapon. Shoving a creature is a special melee attack that does not involve the use of a weapon.
That said, if you also have Extra Attack, the following could be RAW
1) make your first regular attack
2) make your bonus attack
3) stove one of your weapons
4) make the remaining attacks