The text for the bite attack is as follows:

Vampiric Bite

"Your fanged bite is a natural weapon, which counts as a simple melee weapon with which you are proficient."

So since its classified as a simple melee weapon, that means it can trigger the effects of a maneuver, right?

Yep, it should.

There are a few natural weapons which specify that they count as simple melee weapons, so they work with any feature that needs a melee weapon.

The claws given by the Path of the Beast barbarian subclass also fall under this category, and you can even use them as monk weapons!