Pony Clubbers do this all the time for upper level ratings and I have instructions if you want them. There are a couple of considerations, especially if you want machine washable wraps. Is that what you like about no-bows?
Old Barn Rat (love the name by the way!!)
I too was a PCer, and have wrapped with sheet cotton...
I am looking for something washable and re-useable.
My horse chews on bandages, I prefer to use fresh bandages everytime and quite frankly it gets expensive.
I think what I like about the no-bow's are that they seem to hold up well and don't slip as much as even the flannel backed quilts.
If you mean making your own bandages, that's easy - find a tack shop that sells flannel by the yard, buy whatever length you want, and rip at whatever width you like. Simple and cheap. No velcro, but I just duct tape.
If you mean making your own wraps (the thing that goes under the bandages), I'm no help at all!
The upper level kids usually wrap with sheet cotton and cheesecloth so that they can fit their wraps to the unknown horses they'll have at their ratings. Since you're making specific wraps for a specific horse you'll use the same template with different materials.
Use quilt batting instead of sheet cotton as the filler and either use thin flannel (summer pajama weight) or a pillowcase as the cover. I imagine that low pile fleece would work as well.
There are many choices for quilt batting (and I'm not a quilter so perhaps they could provide more guidance), but I would pick a cotton/poly blend mid-loft. I think high loft might be too squishy. Most battings will shrink with washing, so pre-wash before you start cutting for bandages!
Start by measuring your horse from just above the coronary band to just below the knee or hock. That's how tall your wraps will be.
Cut your batting height to the measurements from your horse's leg. Length will be personal preference - if you like your no-bows then use those as a template. Remember the pad should be at least 1" thick when wrapped on your horse, you can double or triple the batting if necessary.
To make the cover with a pillowcase you put the material inside the pillowcase, sew the open flap shut and run a seam or two down the middle of the wrap the length of the material to hold the batting in place during washing.
To make the cover with bolt material (flannel, fleece etc) you cut the fabric 1/2" taller than the batting and twice as long. Double the fabric over on itself and sew the length closed 1/4" from the fabric edge. Stuff the batting in the pocket, sew the open end shut and run a seam or two down the length of the material.
If your guy is a wrap-destroyer you could try wrapping cheap nylon track wraps on top of your standing bandage and flannels.