What do the rules actually say?
What we can see from looking at the rules is that there exists a section on "Moving Between Attack" which explicitly allows you to move between attacks of an action. There is no similar section allowing you to insert a bonus action between the attacks of an ation. Thus, you cannot use any bonus action in-between the attacks of the Attack action regardless of its trigger, even if it has no trigger whatsoever.
This, however, is a rather odd situation and is not something I have ever seen used at the tables I've been a part of, nor is it a ruling I would use at my own tables. Even Jeremy Crawford himself disagrees with this ruling here:
A bonus action that has no trigger—such as Cunning Action and the misty step spell—can take place whenever you want on your turn (PH, 189).
How I actually run my tables
I am all for giving my players more options; if they want to break up their Attack action with Two-Weapon Fighting or some other bonus action, I will always give them that option. This is simply because I don't find it particularly helpful to have some bonus actions able to be used mid-Extra-Attack and others could not be based on small differences in wording that the rules themselves don't even cover.
Otherwise, it depends on whether the trigger for Two-Weapon Fighting is the Attack action or an attack with a light melee weapon
The "Two-Weapon Fighting" section states:
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 [...]
Jeremy Crawford has made the following unofficial ruling (a tweet):
Q. @JeremyECrawford When you take the Attack action, is the trigger for the two-weapon fighting bonus action attack the entire Attack action or a single attack within the attack action? Can that particular bonus action interrupt the Attack action?
A. Here's the trigger for the two-weapon-fighting bonus action: "When you take the Attack action and attack with a light melee weapon that you're holding in one hand …." (PH, p. 195).
Summary: the trigger is the attack that's part of the Attack action, not the entire action. [this summary is part of Crawford's tweet]
Thus, according to Crawford, the trigger for Two-Weapon Fighting is not actually taking the Attack action, but making an attack with a light melee weapon as part of the Attack action. This would mean that you can use the bonus action any time after your first attack of the Attack action.
I believe that Two-Weapon Fighting requires you to actually take the Attack action, and so we can compare this to the Shield Master feat discussed elsewhere:
- If you take the Attack action on your turn, you can use a bonus action to try to shove a creature within 5 feet of you with your shield.
Lead Rules Designer Jeremy Crawford has made unofficial rulings (tweets) regarding the Shield Master feat but ultimately said this:
Clarification about bonus actions: if a feature says you can do X as a bonus action if you do Y, you must do Y before you can do X. For Shield Master, that means the bonus action must come after the Attack action. You decide when it happens afterward that turn.
He also further clarified this here:
No general rule allows you to insert a bonus action between attacks in a single action. You can interrupt a multiple-attack action with a bonus action/reaction only if the trigger of the bonus action/reaction is an attack, rather than the action.
However all of this was then even further clarified with this:
My tweet below was addressing bonus actions and reactions that have triggers. A bonus action that has no trigger—such as Cunning Action and the misty step spell—can take place whenever you want on your turn (PH, 189).
All of these things can be put together and show us that things that use your bonus action or reaction which first require you to "take the Attack action" cannot be done until the Attack action itself is fully resolved. This would mean that you can use the bonus action only after every attack of the Attack action.
Some important differences resulting from attack ordering
Depending on the order of your attacks and what weapon you use, a combatant will have different options. Let's assume the combatant has two weapons, one in each hand, and does not switch out or change weapons. An example:
If they were to use TWF after attacking with both weapons during the Attack action then they could use either weapon for TWF.
If they were to use TWF after the first attack of the Attack action then they would have to use the weapon they did not just use.