Found the right bulk soft bite tubing

[InWithBothFeet]

Amazon.com

This is 5/16 ID, 3/8 OD so 1/16" wall thickness. It is small enough to fit my small bits and stretchy enough for my larger bits. It shipped from amazon, but it took a few weeks to arrive. Cushions the bit without bulking it up and you can cut it to the length you like.

 

[Chasing Embers]

Some have also used surgical tubing.

 

[InWithBothFeet]

I have something similar to that too, but found it to be too thick and bulked up the bit too much for my liking.

 

[kcghost]

Hope you are happy with your find!!