PVC tubes and connectors are great for DIY projects like this. See for example:
Thomas Even Photography Blog: "Tinker Tubes" - Instant Portrait Lighting
For small table top setups, you can get away with thinner PVC than shown in the link. I have a bunch of ~3/8" outer-diameter pipes cut into 1' pieces and a few 90 degree elbow and "T" connectors. They can be assembled into various shapes easily, and then have diffusion or reflective material clamped to them.
Depending on how far away your background is, a reflector might not end up brightening it as much as you'd like. So might also consider adding another flash if you don't have one already. Having separate flashes for the background and subject gives an easy way to adjust relative brightness levels. Just something to consider. Having a tabletop reflector/diffuser setup will of course never go to waste
.