You can add your ability modifier to damage from the bonus action attack
The general rule for damage rolls is:
When attacking with a weapon, you add your ability modifier--the same modifier used for the attack roll--to the damage.
So, you can add your ability modifier here because nothing tells you that you cannot.
Unofficial guidance from Jeremy Crawford (5e's lead rules designer), which some may consider authoritative, agrees with this interpretation (credit to V2Blast for providing this quote):
"When making a weapon attack, you add your ability modifier to the damage, unless a feature tells you not to.
So far, so good.
But, does this rule for two-weapon fighting, which also grants a bonus-action attack, confuse matters?
You don't add your ability modifier to the damage of the bonus attack, unless that modifier is negative.
Don't worry – this rule can be safely ignored. Wielding a double-bladed scimitar, is not the same as two-weapon fighting, and thus two-weapon fighting rules are completely irrelevant to your situation.
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.
Note: Since this question was both asked and answered the text of the Wayfinder's Guide to Eberron has been updated with the release of Eberron: Rising from the Last War. Credit to V2Blast for pointing out these changes.
The rules quoted in the question above have changed for both the Double Bladed Scimitar (slightly) and the Revenant Blade feat (substantially).
The underlying question here is unaffected by these changes - you can still add your ability modifier to damage you deal with the (reworded) special bonus action attack that the Double Bladed Scimitar grants. However, the correct damage would now be '1d4 + modifier', as opposed to '2d4 + modifier' as the Revenant Blade feat no longer grants an extra damage die to this attack.
You can add your ability modifier to damage from the bonus action attack
The general rule for damage rolls is:
When attacking with a weapon, you add your ability modifier--the same modifier used for the attack roll--to the damage.
In short: You can add your ability modifier to your crossbow attack because nothing tells you that you cannot.
Unofficial guidance from Jeremy Crawford (5e's lead rules designer), which some may consider authoritative, agrees with this interpretation:
When making a weapon attack, you add your ability modifier to the damage, unless a feature tells you not to.
So far, so good.
But, does this rule for two-weapon fighting, which also grants a bonus action, confuse matters?
You don't add your ability modifier to the damage of the bonus attack, unless that modifier is negative.
Dont worry - this rule can be safely ignored. The bonus action granted by the Crossbow Expert feat is not the same as the bonus action granted by two-weapon fighting. Thus the two-weapon fighting rules are completely irrelevant to your situation.
Best Answer
Not adding the modifier is a special feature of Two-Weapon Fighting.
The rules for damage say:
Notice there is no mention of this being an attack action or attack with a bonus action. This is the general rule for making an attack.
In contrast, Two-Weapon Fighting has a specific rule:
This rule is specific to Two-Weapon Fighting - it creates an exception to the general rule for damage rolls.1
So you add your modifier to the damage of Soul knife’s bonus action attack since nothing in the ability contradicts the general rule of adding your ability modifier to the damage.
1 The game has a "specific beats general" rule in the introduction to the Player's Handbook which states: "That said, many racial traits, class features, spells, magic items, monster abilities, and other game elements break the general rules in some way, creating an exception to how the rest of the game works. Remember this: If a specific rule contradicts a general rule, the specific rule wins."