If they have your book in-stock it would be easier, then you could speak with the manager. I am sure they have lists

You should consider doing a little actual research on what is involved in a book signing, for both the store and the author. What are the benefits? What are the drawbacks?

Book signings can be a major hassel for stores. Things to consider from their point of view include:

- Who published the book? If it was a self publishing setup, they may not be interested. If you went through a traditional publisher, how many books do they have on hand already? Will you be bringing stock with you to sell and how will that be handled by the store? Will they have time to order extra stock? Will they be allowed to return unsold stock afterwards? Often, a store will want some kind of written agreement on these points.
- are you an unknown author? If they’ve had previous unknowns sit for a low turnout it might not be worth their time and expense.
- are you a local author? There’s a better chance they might consider it, and there’s a good chance at least a few people will show up.
- are you doing signings at other locations? Where?
- what genre is the book? Also, what demographic is your market (as in, if it’s YA or sci-fi, which would be a strong draw to teens, they don’t want to hold the signing durring school hours or the night of the homecoming dance).
- have you let your publisher’s marketing department know ahead of time? Some publishers can provide extra incentives like posters of pre-advertsing for the event, thus relieving some of the store’s financial burden.
- will they allow you to give away or sell other “goodies” like bookmarks and buttons? Some will, some won’t.

You should know enough to at least answer some of these questions (and there are a lot more I didn’t list).

Your best approach is in a business-like manner, not a “look at me ! I wrote a book!”. Ditto at the actual signing. You aren’t just representing your book, but your career, authors in general, your publisher, and the store.

If the store is local to you, you can probably call first to find out who to talk to and make an appointment to meet with them. If it isn’t local, you can call to get the name of the person to talk to, who may or may not want to discuss it by phone (if not, you will need to send a letter).