Be ready. If things start to go your way, if the readings start to happen, and then talks and other kinds of appearances, people will start to ask you for a publicity packet. If they don't, they are still nevertheless secretly hoping you have one. It will make their job much easier.
The idea here is simple. In some kind of professional-looking folder--anything nice, really--assemble a photo, a short bio or a press release, a list of your publications with your publisher information, and a page of reviews. There are variations of this, but you get the idea. You might add a longer vita if it's appropriate, or a book jacket.
The photo and bio, and anything else like a book jacket, will go into publicity--posters and handouts. These, along with selections from the reviews, will go into newspaper articles. The list of publications is for the local bookstores, so that when you get there you will actually see some of your books for sale. You'll probably hear the bio verbatim when you are introduced.
Helping your hosts help you is good for everyone, and with a little planning everybody looks professional and on the ball. But the real secret to all this is you doing this work ahead of time, in a considered and diligent fashion.
DVICE. Get a few of these publicity packets together now. Having something to hand out whenever you are asked is the mark of a cool cat, like you were ready for this and do it all the time. A few photocopies and a few folders and a few photographs all together don't cost much, but add up to a great deal. And if something changes, it's just a few more photocopies.