Secure the center of the LED tape to the center of your handlebars, positioned around your stem. If your handlebars aren't attached to a stem when you do this project, add something to occupy its place, like rolled up cardboard and a velcro tie.
Cut the backing strip near the stem to expose the LED strip's adhesive. Peel away the backing as you affix the strip in position on the handlebars.
1m of LED tape covers these drop bars nicely.
Clip off any extra LED strip with your snippers.
Repeat with the other side.
Wrap handlebars with clear grip tape. I found it on Amazon in two colors (neither of which gave the LEDs any discernible tint).
Test out the LEDs with a reliable 12V power source. These drop bars were adorned with 1m of LED strip, while the bullhorns below have 2m spiraled around them.