I use dental floss myself, the way I do it is start by tying a overhand knot in the floss just below your knock set, then tie
Another overhand knot 180 degrees ( just opposite) the knot you just tied, then do this alternating knots down the string until you get as far as you want, usually about 3/8" or so. Tie a double knot the last one you make and trim floss a little long and burn the ends until they are flat.
I've been doing this a long time, works great, they eventually wear some, but are easily replaced. This works much better than just wrapping it around the string.
I would also suggest you learn to tie on a string serving, very easy, and you will have the ability to replace the serving with a different diameter string. This is a more permanent fix.
Good luck,
Roy