I recently graduated and now working on getting a start-up going at the moment. I've wanted to pursue graduate school and I like the research aspect of it, and I've done undergraduate research as well.
I have several ideas which are a bit more hardware/software mixes and more research oriented, and no patents exist for them either, so the first answer is walking the patent path and selling the prototype/idea or have it bought out.
Other option: Is it recommend or even possible to pursue a graduate degree with a focus on researching on the said personal idea? Any remote chance a professor/group might want to entertain my idea (in which case I wouldn't mind if the project gets merged with the school)?
With this freedom, myself and another graduate student began our own laboratory within the department that focuses on medical technology for developing countries. We have been able to convince undergraduate students, as well as graduate students to work within our lab for free. We have also set up an internship program, where students outside of the university can join. Our professor was also happy to put his name on grant applications for our project.
In my experience there are two types of potential professors. First the ones that are interested in their own research - in which case you are required to do something for them. Or the other (old skool) professors who think you should go about getting your degree on your own. The problem is this second type generally does not come with any type of funding.
My overall advice would be to pursue graduate school, especially if you need for time to work on your idea. Graduate schools have excellent resources to help you with your company (especially within this economy).
P.S. I'm actually involved in a start-up company right now while attending school. Perfect opportunity to incubate your idea while you wait to develop.