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.