For drill bits, it is pretty straightforward to take a block of
wood and drilll a series of holes that suit the bits, deep
enough to leave only half an inch or so protruding.
Then you can route or chisel out another block to be a lid, and put it on with a hinge on one side and a catch on the other.
Driver bits being sommuch shorter, but generally less varied in diameter, you can do pretty much the same thing, with a smaller base block. Helps make it easy to know right off which you have, the drill bits or the screw drivers.
For screws, bolts, nuts, nails, rivets, wasshers, lock washers, cotter pins and whatever other small bits you need, baby food jars are a classic option, but there are probably a hundred different versions of little bins in racks.
Fishing tackle bixes are another remarkably adaptable option, with loads ofnvariety to choose from. For easily portable toolkits with assorted supplies they can be a really good option.