I think the decision of whether to bring more books or not will depend on how many you think will be attending the event. Do either you or the bookstore owner have an estimate? That should help determine need. But I will say that it's tough to estimate for two reasons: 1) You're a new author; and, 2) With no book signing experience, you have no idea of what to expect in terms of numbers. Are you making them RSVP to the event? If so, that can help get a better handle on the numbers.
Also, the bookstore owner may not allow you to sell books direct to attendees since they may feel that you're trying to get out of giving them revenues or commissions. Don't do it unless you have express permission from the owner.
If your estimated amount of attendees (especially if based on RSVPs) is higher than what the owner is stocking, then you need to have a conversation with them about what to stock. Be aware that they may not be amenable to buying more inventory, especially given that you have no track record.
You might also want to have a conversation with the bookstore owner about signing event sales exceeding the on-shelf inventory. Could there be a way for these attendees to purchase the book at the event and have the book shipped to them or sent to the store for pickup?
Not all attendees will buy your book at a signing. Plus, it is VERY difficult to get people to attend live events like these, especially for unknown new authors. So I think you can understand the owner's caution.