When making my binding I wind it onto a Binding Baby. I also have the spindles for them, so that I can set them by my machine when I am putting on the binding. I have two, a large one for long bindings and a smaller one.
Binding Baby Some people put their binding baby on their extra sewing machine thread spindle, but I prefer the stand alone spindle that is made for it. I bought mine at an online quilt shop quite a while ago.
Here is a video by the 'The Crafty Author' the Binding Baby with the spindle is toward the end of the video around the 13 minute/14 minute mark.
The Crafty Author