Getting a white background (or black background, or just about any other background effect) is about lighting the background and the subject separately.

So my advice is:

1. Dump the lightbox - it simply isn't a good fit for white background photography (too small and doesn't let you light the background).

2. Get a cheap flash like the YN-460 (about $40) + some way to trigger it off camera (a cheap set of radio triggers will be less than $20, a cable may cost less) + a small sheet of glass or clear plastic

3. Attach the glass to something so you can use it like a shelf, but the bottle on the glass, position the camera so all you see is the bottle, the glass and the wall behind it.

4. If the wall is dark you may want put cover it with something that is lighter in color, it doesn't have to be white, just a light color.

5. Set the camera to manual mode, set a nice middle of the road aperture (around f/8) and set your shutter speed to something equally mid-range-ish (1/50-1/100)

6. Put the flash near the back wall pointing at the wall, take a test shot, dial down the power until the minimal power that still over exposes the background (the bottle should be too dark at this point)

7. Add your lights, set them to light the bottle as much as you want, adjust shutter speed (and not the aperture or ISO) to make the lights lighter or darker - the shutter speed will effect your continues lights but will no effect the flash, as long as you stay below the sync speed (typically, 1/200-1/250, depending on camera) - if you need to adjust aperture or ISO you will need to also change the flash power to compensate.

I blogged about it a while ago at: http://www.usefulphototips.com/2011/12/20/making-the-background-white/ you can see examples and setup pictures there