95% of the time I'm using 1-2" bits, so I store those in a way similar to the OP and many others here. I keep a second plastic cased set in my go bag for jobs done away from my shop. I don't use 4-6" bits that often and good quality long bits are quite expensive, so I only have one set. I store them compactly in one of those plastic sleeve tubes that often come with new rotary hammer bits, core drill bits, ship auger bits, milling cutters, etc. I don't know what those plastic tubes are officially called, but they come in various sizes and diameters. Some are round and they have a top that twists off and others are square and have a top that pulls off but has resistance notches along the corners.
I cut my spare storage tube down so when the top is off the bits stick out about an inch or two so the tips are easy to see and grab. The tube normally sits in my main tool chest bit drawer, but I grab the tube and toss it in with my other travel tools if I think I might need them for a job done away from my shop.