Hi Peter,
Interesting project.
At a guess I would say that you have a light leak as a neon bulb should only generate discrete emission lines, no continuum. It is possible that there is a problem with the neon bulb, but I think a light leak is more likely.
You could try taking 2 exposures of the same length, one with the neon bulb turned on, and the other with it turned off.
The other effects that can cause an offset are dark current and bias offset, but they should be roughly uniform, not showing the hump you seen in your spectrum.
Cheers,
Andy