Is it appropriate for an undergrad student to ask a professor to sign a non-disclosure agreement?
I don't understand most of the current answers, which mostly assume you want technical advice without paying for it, but requiring an NDA. If this is indeed what you want, I agree it's a bad idea.

However.

You write that this professor has already gone into business. This implies that he has a certain basic understanding of how business works. He probably has signed his fair share of NDAs, as well as requiring others to sign his.

It appears perfectly reasonable for you (or your friend) to set up a short meeting with this professor, say of 30 minutes or so. Quickly present your idea in a rather general manner, in an "elevator pitch" - at least outlining what problem you want to solve. Think beforehand how much you are comfortable revealing. Tell him that you'd like his advice, and be frank that you are not comfortable giving full details without protection for your intellectual property. (I'd also look for protection if I knew this professor, not only if he were unknown.)

Have a proposal ready for possible next steps, which would include him signing an NDA and his investing a little time for a discussion. Ask him explicitly what he'd expect from you in return for investing his time. Professors are busy people, and more so if they run a company on the side. 

You may actually have a good chance that he'd be happy to mentor you to a limited extent pro bono - most academics are idealists at heart, otherwise they would be in industry from the very beginning. However, if you want more in-depth advice, be prepared to offer hourly rates, possibly conditional on your idea getting off the ground.

Always keep in mind that professors are busy, just as are other businesspeople. Don't come with a mindset that you are entitled to advice, but ask politely, and things may go well. If this professor is active in a similar line of business as you are, this may be a very good opportunity - he may have contacts in the industry and/or to funders that may very well be invaluable.