It's a tricky, frustrating proposition!
I haven't mastered it. I can do a four-turn wrap OK, but the smaller ones are tough. I've managed a few 2-turns, but it was a pain.
Here's what I do for bamboo, particularly the older ones that had wider wraps than today.
I set up the wrap as normal, but don't cut the tag end. I make my four turns (or whatever number you feel comfortable with) then pull the thread under with my loop. What you end up with is both tag ends protruding, and you can gently tug on them to tighten the wrap and pack it. Make sure to tighten from the direction that the tags are running. The tricky part then is trimming them. I use a new razor blade, hold the tag end tight, and gentle trim it flush with the wraps. For the other tag, I gently slide the razor edge up against the wrap, perpendicular to the blank, and gently roll it over the tag to cut it.
This doesn't always work, and you have to start over!
If you end up with a slight nub, it'll disappear under a few coats of varnish, and you can trim it down when the varnish hardens enough. Then finish it out as normal,
Hope this helps,