This is the problem I set out to solve.
I've made a small 3D printed key chain which can hold any regular hex bit. Keeping one or several of these with your keys will solve the desperate rummaging for whatever item that can somewhat act as a screw driver.
How to make it can be found in this instructable.
I modeled the file in Fusion 360. I'm growing fond of this modeling software, and I'm learning several new tools and techniques every time I use it.