Inspiration from this came from the Stubby magnetic bit holder by AldiPrinter.
I liked the look and feel of this, but didn't want to be chasing bits all over when I needed them, so I added bit storage inside of it. Because of the extensive changes that were needed, I recreated the model from the ground up as a solid model, and then created the .stl files.
The thread is actually a custom rolled thread like what is used in electric light sockets and lamp bases, which works surprisingly well for 3d prints because no part on the thread is less than a 45deg angle to the base, so you don't need to worry about supports or poor thread surface quality when printing.
I wanted this to be strong, so I printed with 6 walls, 6 base layers, and 6 top layers. At this many the infill doesn't really matter, but I did 75% anyway.
Print the screwdriver_base model with the bit-end down, and the screwdriver_cap model with the bit-end up, and no supports will be needed, as the only real overhang is at the base of the hex driver, and that's short enough and hidden that some minor bridging imperfection isn't a big deal.
If you get blobs on the inner surfaces, the bits might stick, so either just scrape them away, or optimize your retraction, coast, and wipe settings to avoid them.