Excellent suggestion...having one of their books, means I am willing to put money in their pockets, and wanting the autograph, will, as you say, flatter them...
The plot thickens...this is fun...
Besides asking for your book to be autographed, be sure to ask for a catalog of what they have that's available. That should be free, and they'll be delighted to give it to you. Oh, if the author of your book isn't available, ask if you can leave it with your address and some money for postage (that's important!), so he can sign it when he's got time and send it to you. Bring an address label to make it easy for them. They'll have to regard you as a serious fan.