While I usually do solder the ends together when I tie a bezel for a
stone, there are times when I don't have to. The important thing to
keep in mind is that the bezel has to maintain its integrity around
the stone, so merely bringing a strip of braid around its perimeter
is not going to provide much security.
I make the kinds of bezels you refer to above, from as small as 6mm
up to any size desired, but it isn't a trivial thing to do. The knot
that I use is the Turk's Head, which you can learn to do very easily
from a number of books (I recommend the "Ashley Book of Knots", but
there are many) and it's just a matter of producing it in wire at the
I teach people to make them as finger rings, but it's just as easy
to measure the circumference of a stone as it is to measure a finger.
My website has enough on it that at least a few people
have learned to do them on their own, without taking my workshop,
just from looking at it.