Twine is a little bit coarse. I bought a roll of waxed nylon for whipping, it works pretty well, but you need to wrap it around an awful lot of times to get the desired thickness.
If you have some old stable braid rope laying around, the individual strands from that make pretty good whipping string. Then you can melt the ends down a little bit with a candle (on the whipping, not the Bee Line), and it will be there forever.
I guess you discovered that you can't melt the end of that Bee Line to make it stop fraying, eh?