You can use cloth tape on the handlebar to increase friction so the mount is more likely to hold still. A good-sized roll is $2 at the pharmacy/general store. You can magic-marker it black to match your bars or if it stands out too much.

One nice thing about bike-specific headlights is the beam pattern that spreads the light out to the sides and, on some, keeps the beam shining toward the ground and out of people's eyes. In my opinion the spread beam is really nice, you do want to see what's off to the sides.

I rode for a while (a short while) with a round flashlight beam and it was hard to make tight turns, like within the width of a neighborhood street, because I lost orientation information from the sides and it blew my balance. The bright light made everything else seem darker, practically invisible. It really cut me off from everything around me. I felt more connected to the world with lower levels of lighting, without the bright flashlight. There are diffuser lenses you attach to the flashlight to spread the light around, and I have a couple on order to try out, but I don't know how well they work yet.

Here's a cheap way to keep from blinding other people: How can I protect my Raynauds' hands from windchill?

Here's a guy who made a flashlight handlebar mount out of a soft drink bottle. I don't know though, that looks like a lot of work, and the TwoFish one looks more sturdy.