I believe perhaps you are making some false assumptions, specifically:
1) You need a job to get a mentor - not true. You can start your own business and still have mentors. You had mentors in school didn't you? If you want a mentor, focus on finding a mentor, not a job. You can find both business and technical mentors.
2) You need a job to learn - while it is true that on the job training and practical experience are valuable, they are not the only way to learn. Where would we be if Bill Gates had decided to work for a big company first instead of leaving college to start Microsoft?
The questions I would suggest you focus on are:
1) Does your "wonderful idea" make business sense? Is there a good possibility that if you work on it that it could lead to the point that you could make money with it? This is your reality check.
2) How will you live while you work on your idea to the point where it will support you? If you can live at home and your parents are happy with that then great, I would say give yourself 6 months to 1 year and go for it. When you get to be 35 with a wife and 2 kids it is unlikely that you will be in a position to take a year off without pay. Do it now while you can. Assuming you work sincerely and diligently you will learn a lot and get invaluable experience in that 6 mos to 1 year. Of course if you party every night and hang out with your friends during the day it is another matter....
At the end of the year (or whatever amount of time you gave yourself) you should have a very good idea of how well you met your goals and if it looks like the business will be viable. By this suppose you estimate it will take 8 months to build your product and another 4 months to get enough customers to make it viable as a business. Now at the end of a year you found it really took 10 months to program and that you have just a few customers; well you would clearly see that it is worth sticking with the business for another 3 months to see how many more customers you will get. If on the other hand at the end of the first year you are only 20% done and someone else has just come out with a product like yours only better then you know it is time to go do something else. Even in this case you will have gained valuable experience.