We’d sometimes buy the most used blades in bulk and just hang them up on a pegboard on the side of one of the cabinets in the tool room at the workout center. When picked up by the crews, these blades probably just landed in the tray of an odd toolbox in the back of one of the trucks. Alternatively, some blades that we did not stock, might get picked up the day of the job at one of our suppliers or Home Depot.
At home, my assortment is just jumbled together in a plastic toolbox - not the best organized sort of thing!
I guess that you might expand on the storage ideas used in this Bosch set:
A canvas tool roll might work for you:
There are lots of different ones on the market.
You might also cut some PVC pipe into different lengths to accommodate different blade lengths. A fixed pipe cap at one end and removable one at the other.