You have lots of options for fringe and a strap. The fringe on this bottle is meant to echo the organic nature of the pattern. It was arranged around the bottom of the bottle in varying lengths, each with a different dangle. In most cases 3 or 4 layers of staggered fringe with the longest strands in the middle and the shortest at the outside edge would work well. Also, a tassel hanging from the center of the bottom instead of fringe would look great.
The strap is a simple design. The thread is woven to one side of the lip of the bottle, strung on a long strap with groups of ten mixed 11/0 seed beads separated be one larger bead. The strap was attached to the bottle beading at the sides. This is obviously only one option. Another would be to attach jump rings on either side and use a chain or a strung necklace for a strap. Check out this article on Beaded Strap Ideas for more possibilities.
If you'd like to try your hand at designing a pattern for one of these bottles, here are some graphs for you to use. The graph for the body is only 21 beads tall. The height of the bottle is more like 24-25 beads. You might try using several rows of a solid color at the top until you get used to decreasing. That way you won't mess up your pattern.

