If this is possible how would I go about doing this?
Yes, it is possible but very very uneconomic.
Computing power is not a form of energy, is a way to consume electric power transforming it in heat (which is a disordered form of energy).
A bulb is just another machine that transforms ordered energy (electric power) in disordered energy (light and heat). Not so different from your CPU.
You can get ordered energy back from disordered energy (with a thermal power plant) but only wasting most of it: http://en.wikipedia.org/wiki/Entropy
I know that it's not efficent I'm not looking to be powering it for a long time but just to know that it can be done and I think it would be a cool thing to do.
One way or another you will require the inverter.. and the shortest route to take without blowing anything is usb..