Scimitar of Speed with Two-Weapon Fighting?

Question

So I have a Bladesinger and I just picked up a scimitar of speed.

Normally in a melee, I pop a shadow blade(SB) and Two-Weapon Fighting with a dagger. I don't have the dual wielder feat, so I don't get +dexmod to damage with the dagger.

If I were to use SB with the scimitar, does using the scimitar's ability to attack as a bonus action give me +dexmod damage if I used SB to attack with my action? Or does it fall under Two-Weapon Fighting?

Answer 1

you can make one attack with it as a bonus action on each of your turns. (DMG 199)

This is an ability granted by the weapon itself and is unrelated to two-weapon fighting. Notice that you do not need to wield another weapon to use it. The rules of two-weapon fighting thus have no bearing here. You add your ability modifier as normal for an attack.

Answer 2

You don't have to use Two-Weapon Fighting

You are certainly allowed to, according to Player's Handbook page 195, under 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.

However, this rule states neither that this is the only way to attack with an off-hand weapon, or that it must be used when attacking with two weapons. The Scimitar of Speed gives you a better way to attack with a bonus action, on Dungeon Master's Guide, page 199:

...you can make one attack with [the scimitar] as a bonus action on each of your turns.

Since this rule allows you to make a bonus action attack without the rules of Two-Weapon fighting, you will get your dexterity modifier included in the damage.

Note that like the auxilary attack of Two-Weapon fighting, the scimitar's bonus action attack is a single attack, not an Attack action: Extra Attacks and other abilities that trigger based on Make an Attack action are not triggered.