I am just putting the finishing touches to my shop, and came across a real PITA. So I decided to do something about it.
These are the main PITA bits, always stuck on top of the lathe, ready to drop down onto the chuck to get themselves launched into space. The chuck mounting key, the chuck key and the allen key used to tighten up the cross slide. There are a couple more bits, but I will show about them later.

I grabbed a piece of 1/2" thick PVC plate (it could be almost anything, even a bit of thick ply, as long as it is strong enough).
Ignoring doctors orders, I got onto my mill and did a bit of work on it. The half round recesses are not totally necessary, you could just use normal slots instead, but don't go too deep, just enough to stop things jumping out of the slot. I rounded over every corner, just in case. If and when I bend down, and if my noggin catches it, or if I bang into it, I won't do too much damage (to myself, not the tidy).
This took me about 3/4 of an hour to get to this stage, it doesn't need to be precise, just good enough to retain the bits.

This is where I fitted it onto my machine, you would have to find your own ideal place, maybe mod it so it sits on the wall, but within very easy reach, so that it is just as easy to drop things into the tidy rather than sitting on or around the machine. I used this sort of thing on industrial machines, and after a few sessions, it becomes automatic to use it.
It only sticks out by about 3", so really it doesn't get in the way.

And this is how it works, a place for everything, and everything in it's place.
I have yet to make a swish swarf rake to match the other ali handled bits, but when I do, it will drop into the hole allocated for it.
You might say that the door on the stand won't open fully now. All that are in there are my steadies, so if I do need one, it will only take a few seconds to clear everything out of the tidy.

Simple, easy to make, and makes the shop just that little bit safer.
What more could you ask for?
Bogs