We just had our auction, and it's the second year I've helped with the soliciting. Last year I was uncertain and nervous about whether or not I could do this, as was one other person (our committee had 3, so 2 of us were complete newbies.)
A letter is a must. Often the person in the business you're visiting is not the owner or manager anyway, and they can only pass the info on.
If you have at least one person who has done this before, maybe they could tag team for a bit so the new person feels more comfortable.
Make sure in your spiel you let them know what advantage they could enjoy (i.e. - "Our school has over 700 families, and the auction is our largest and most popular fundraiser.") Donating is a form of advertising, and they're business people, not charity wards, so inform them of how many eyes will see their stuff.
In the end, I found it moderately fun, very tiring, and kind of humbling. I got an entirely different view of the community I've lived and shopped in for a good number of years. Many businesses are VERY open-handed, and this despite the fact that they're often hit up for donations, sponsorships, etc. In some cases, I've changed where I do business because one place has donated and another hasn't. If I try a new restaurant or shop because I heard about it at the auction, and I get a chance to chat with the owner or manager, I tell them that's where I heard about them. Every little bit helps, and it's sincere.
If there are people who might be willing to try to solicit, you could do worse than to have someone who has done it before give a little pep talk!