What do you think is the best way to approach out of area bookstores about signings? For example, if an author will be traveling somewhere and would like to look into a book signing, is the best way via a phone call, email, letter?
Well, according to my experts, there is no good way. Bookstores are reluctant these days to book any children's booksignings whether they are in or out of area. It seems they don't think anyone comes to them. The bookstores then feel embarrassed and they are left with extra stock on hand that they can't return for 90-180 days. If you want to do something at a bookstore, you'll have to sell it to them as an event. For younger readers you can do a story/activity time. For older readers, you can do a reading or a writing workshop. If possible, try to have the local SCBWI sponsor you in some way. This will at least get your visit publicized to its membership.
Once you've decided they program you would like to pitch to the store, call and ask for the manager for small stores or the Community Relations Manager/Specialist for large independents and chains. They may not be able to speak with you right then, but you can schedule a time to talk. Then pitch them the idea. The worst they can do is say no. Also, be sure to try and schedule at least 3 months in advance. This will guanrantee that you will make any promotional or advertising material the bookstore produces.
School visits, which isn't specifically quoted in the question, but the person also asked about those, work in a similiar manner. After you have researched the districts and private schools in the area you will be visiting, you just need to start cold-calling librarians. Have a prepared script, but don't be afraid to deviate from it. Also, follow up any somewhat positive leads with a mailing of either a brochure or letter with brochure.