I have a bag of blue jeans selvage from Pendleton Mill that works great as weft for mug rugs. It adds an interesting texture and weaves up quickly.
I warped up a board with natural cotton rug warp. I used blue jeans selvage in a basket weave pattern as weft with tabby shots of cotton rug warp between. Here the tabby is bubbled before beating with the tapestry needle.

tabby weft with bubbling
Here the blue jeans selvage weft is pulled straight while holding onto a loop at the other end. This keeps the mug rug from pulling in.
blue jeans weft pulled straight
And here's the finished mug rug. Note the hem stitch. I won't take it off the board as yet because I can weave a second mug run on the reverse side.
mug rug with hem stitch
I won't take it off the board as yet because I can weave a second mug run on the reverse side.
warp on the reverse
sample rag woven mug rug
The weft is cut from strips of fabric.
~*~
Supplies:
canvas art boards
self-sticking label squares
cotton warp
bamboo skewers
tapestry needles
blue jeans weft
scissors
6" ruler
ziploc baggies
pencil & paper