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I am using the double-bladed scimitar with the Revenant Blade feat from Wayfinder's Guide to Eberron.

The double-bladed scimitar's special feature (p. 74):

Special. When you take the attack action and make a two-handed attack with a double-bladed scimitar, you can use a bonus action to make a melee attack with the blade at the opposite end of the weapon. This attack uses the same ability modifier as the primary attack. The weapon’s damage die for this attack is a d4, and it deals slashing damage.

The part of the Revenant Blade feat (also on p. 74) that mentions the damage:

On your turn, when you use a bonus action to make a melee attack with the blade at the opposite end of the weapon, the weapon’s damage die for this attack increases to 2d4, instead of 1d4.

Let's say I have 16 Dex, so a +3 to my dex mod. If I take the Attack action with the weapon, and use my bonus action for the weapon's special function, do I add my Dex modifier to the damage of the special attack or not? Will it be 2d4+3, or just 2d4?

Based on the wording alone, I think you have answered your own question.

This attack uses the same ability modifier as the primary attack. The weapon’s damage die for this attack is a d4, and it deals slashing
damage.

and

the weapon’s damage die for this attack increases to 2d4, instead of
1d4.

So because of this, you would get 2d4 + ability mod.

You can add your ability modifier to damage from the bonus action attack

You can add your ability modifier here because nothing tells you that you cannot.

Two-weapon fighting also grants a bonus action, which I think may be confusing you:

You don't add your ability modifier to the damage of the bonus attack, unless that modifier is negative.

However, wielding a double bladed scimitar, is not two weapon fighting thus two-weapon fighting rules are completely irrelevant here.

Add your ability modifier to damage rolls as you would with any normal melee weapon attack - your damage roll with this bonus action will thus be 2d4 + 3.