You can only take one bonus action per turn.
The rules for bonus actions state:
You can take only one bonus action on your turn, so you must choose which bonus action to use when you have more than one available.
So no matter how many attacks you can make with your action, you can only make the attack from Two-Weapon Fighting once per turn, because it uses your bonus action. Even if you use Action Surge to get an additional action on a turn, you still only get one bonus action on your turn.
So suppose you are a 5th level fighter. You have the Extra Attack feature which says:
Beginning at 5th level, you can attack twice, instead of once, whenever you take the Attack action on your turn.
So if you were wielding two short swords, you could use your action to take the Attack action, making two attacks using either of your short swords (the order doesn’t matter, it can be one each, or two attacks with one), then, you can use your bonus action to make an additional attack using Two-Weapon Fighting:
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.
Then, as a fighter, you could use Action Surge to take an additional action on your turn, and use it to take the Attack action a second time, making two more attacks. However, Action Surge does not allow you to take an additional bonus action. So even if you use Action Surge to get an additional action, you still only get one bonus action per turn.