How to reduce vibrations to handlebars on aluminium road bike
I have an aluminium bike with a rubber dampener built into the handle bar, it's part of Specializeds range, not sure if there are general versions.

A suspension fork would iron out more bumps than a carbon one, but may not fit your bike.

I've taken videos from a handlebar mounted camera too and I think there will always be a lot of jolting that is impossible to dampen. Low light will make this worse.

I think the best answer is to use a helmet mounted cam, so the suspension system is your body and neck. I've seen some fantastic videos of the New York alley cat races and they all use helmet cams. They also need strong necks!

How much image stabilization can your camera provide?