I don't know if it's authentic, or if anyone thinks it's great except Grant Peterson, but here's a link to pictures & diagrams of his preferred method of finishing off bar tape using hemp twine:
http://www.rivbike.com/
Dave Ross Portola Valley, California, USA
PS probably some types of dental floss would work, too.
Rob asked:
"... Also - what is the best way (and period correct way) to finish off the tape
at the bar center? I don't want to used an off-topic electrical black tape
type deal. How was it done in the fifties and sixties? Was there anyone ou
t there with a great inovative method?"