Flexible Wax Craft

I sew little tea bags out of cloth for my loose tea. I include two strings which tie nicely around the handle of a cup, but the tea always soaks up the strings and then dribbles down the teacup.

Any ideas for something besides a traditional string? It has to withstand temperature (no waxed string), not be conductive (hot tea = bad, for example, metal), and be flexible.

Thanks Yahoo community!
OK, to clarify, I create a tea bag which is basically muslin with a draw-string on top. I can fill it with loose tea leaves, steep the tea, then remove the bag when it's done, rinse the leaves out, let dry, and ready to re-use. I have strings sewn on both to close the tea bag, as well as to tie it onto a cup handle so I don't have to fish it out ; also keeping the top of the tea bag upright keeps any stray leaves from coming