Chosen Solution
If you’re anything like me, your fingers aren’t needle-nosed pliers. I struggled to remove the tightly-packed bits until I wrapped a rubber band around it and then easily pulled it out. Now whenever I open the kit up, I make sure to have a rubber band nearby so I can quickly and easily get to the bit I need.
Thanks for the advice oldturkey03 :D Here’s that: iFixit 26 Bit Driver Kit Technique for Removing Bits
I always put the handle over the bit I want to remove, pull outwards and then upwards, remove the bit from the handle, turn it around, put it back in, and presto :)