You want to save a minute of time when sorting to toss or donate fabrics? I use a tall kitchen trash can to hold the bags when I'm sorting through donated fabrics. Very often the fabrics are unusable. It might be the wrong kind or dirty or dry rotted. The can holds the bag upright and open for me so all I have to do is stand back and toss toward the right can.
I usually put several bags in the cans before starting. That way, when the bag is full.... all I have to do is tie it and remove.... the next bag is already there and ready to use. I don't have to stop to open another bag.
I do this for all the trash cans around the house too. The ones in the kitchen, bathroom, bedroom, and sewing room all have several bags in them. This saves time when cleaning house. This also saves space because instead of the trash bags taking up space in my utility cabinet... the bags are where they will be used.