I put my screened batches and final mix back into the same bags I bought the mix or bark in. I save those bags from year to year, but sometimes slice them up for lining the walls of my raised beds lest they dry out too fast. Once I used it on the bottom of a raised set on top of some agressive roots. That bed stays moist longer than any other bed I have!
Often the bags I buy bark, grit or mix in are stronger than the cheap garbage bags I buy.
>> I mix the two together in a wheelbarrow
Always! And I happened to wind up with two wheelbarrows through luck not planning, but they are a HUGE convenience when screening and mixing.
If I have to bend over or stoop frequently, I poop out much more often. But I found that I can do some shoveling and screening while sitti8ng on a floding chair, with a thick, stiff cushion.