I used 2 mm spectra for the line (as resistant as you can get),
3/8 tubing,
and a 250 pound swivels.
This is a bungee I make for euroguns. Here it's on a carbon version of the Dessault Quatro.
Notice how the tubing material dampers potential metal noise.
The 2 mm spectra fits smugly. You only need to make a knot on the other side. It's a very clean look.
For the wooden guns, or gun I equip with a reel once in a while I use the standard two loop bungee.
Here is 40 of them.
Same eurostyle system on a Marc Valentine with a bow type knot so I can take the bungee off fast.
They are available at Charlie's Narrangansett Pier Diveshop.
www.renepotvin.com