Don't use a zipper.. yuck..
If you plan on bivying on the ground in your hammock, then velcro on both sides. I really like being able to get in *either* side so I don't have to worry about which way I pitch it, depending on what I'm hanging over. it doesn't matter if you're hanging over flat ground, but if you get a bit more creative on where you hang, it's nice to be able to get in either side.
On the other hand, my first suggestion is don't attach the bugnet at all! make your bugnet so it will go over a ridgeline, and hang down over your sides. put a few pockets in the sides of the bugnet that you can put some rocks or sticks or coins in,and you're done. the hanging bugnet will be against the sides of your hammock and you won't have any issues. I've slept in one like this in horribly buggy conditions without any problems.. just make sure the ends of the bugnet are together (velcro, snaps, duct tape etc) so they
aren't coming in the ends. but really, when you're hanging you don't need the bugnet attached to the hammock to keep the bugs out. you just need it against the side of the hammock.