They are called Thread Nets. Ask for them at any store that sells ME thread.
When I had my loose cover business, on my over locker. I have a plastic bag just a bit bigger than the big cone of Bulk, hole at top and bottom , and worked a treat try it see if it works for you.
When you purchase fresh garlic in a three pack plastic net - it is the right size for medium and large spools of thread.
And didja know you can use old panty hose or knee hi's? Cut to length ...roll edge.
I went to several places that sell fresh flowers, and asked them to save the nets the flowers come in for me. They were all happy to do this. I went back and picked a lot of nets the following week. I washed the ones that were a little soiled. I now have all the nets I need, for free.
I've never seen flowers come in nets, but that might be a regional thing - I live in western Europe.
That is what I use too. The flowers are shipped in these nets so you will have to ask if they have any.
I'm a florist and use the nets! Mops, you may not have seen them because they are removed by the florist before the flowers are sold. They are to protect the blooms for packing and shipping.