Can a warlock cast magic stone on 3 pebbles as a bonus action then subsequently cast mage hand to fly the stones over an enemy and drop them to deal 3d6 damage on hit? If so, what, if any, would be the modifiers applied to them? If not, then please explain why.

Mage Hand cannot do this

There are no rules that allow things to be dropped to deal damage. A GM may allow it (and this question reveals the lack of rules for this situation while this question discusses how non damaging a small object like a pebble would likely be.), but you would not use the modifiers from the spell because:

You or someone else can make a ranged spell attack with one of the pebbles by throwing it or hurling it.

Not only is the mage hand not "someone else" (it's a spell effect), dropping it doesn't qualify and mage hand is unable to make attacks...

The hand can't attack, activate magic items, or carry more than 10 pounds.

Even dropping the rocks should be considered an attack which makes it impossible for a mage hand to accomplish.

If your GM does allow it, it will be up to them what modifiers to use.

No. Magic stone requires an attack to deal damage, and mage hand can't attack.

From the description of the magic stone cantrip:

You or someone else can make a ranged spell attack with one of the pebbles by throwing it or hurling it with a sling. [...] On a hit, the target takes bludgeoning damage equal to 1d6 + your spellcasting ability modifier.

From the description of the mage hand cantrip:

The hand can't attack, activate magic items, or carry more than 10 pounds.

A generous DM might allow the trick. He'd have to define the mechanics - but 3 * (1d6 + spellcasting ability modifier) damage seems way too much for a 1-round cantrip routine.

First I test the "drop stuff from the mage hand range" and then apply it to the D&D gameplay.

Physics!

Dropping a 4kg stone from 7 metres (2 metres enemy height) roughly has 240J energy.

per http://home.earthlink.net/~jimlux/energies.htm

That is roughly the speed of a fastball travelling at 100mi/h which means quite a lot of energy.

If You could reliably hit someone unprotected from the top while they're not paying attention, you could reliably take them out.

I would allow it, but any headgear like helmets would greatly diminish the effectiveness of this (prevents the knockout), and while a human, elf or halfling head would be vulnerable, a giant, troll or orc would not.

Also, I would not deal damage. It would not be usable in combat. At all.
For narrative reasons a surprised person would be susceptible. A great way to start off the fight. Also, 4kg stones might become a rarity, I mean if it's 2kg, the energy is to small to cause much damage, and at 5 it's too heavy to lift.

Imagine a mason story that once during a war there was legislation to remove over-2kg and sub-10kg paving stones by cracking them due to prevalence of mages dropping stuff on peoples heads.

Also, a "morningstar ball" weighing 4kg might be a mage hand weapon of choice.