Since a light bulb will run happily on AC, it's unlikely your headlight has any sort of rectifier built into it. You'd be best off doing something a little fancier than a basic bridge rectifier. Some capacitance will smooth things out. Here's one example, there's lots of others on the web:

Dynamo Powered LED Bike Lights: 7 Steps

I'd imagine that someone must sell some sort of LED unit with a built in regulator that could be shoehorned into your old light housing. That would be the easiest way to go.

It would be a good idea to determine your dynamo's voltage and current output before proceeding. Got a multimeter?