Can I supply a 12V buzzer with 18V?
Devices have voltage ratings for a reason.  Usually a higher voltage will damage the device.  Look at the datasheet and see what the real maximum operating voltage of this device is.  Perhaps 18 V is OK, but unless it explicitly says so for a "12 V" buzzer, you should not assume it is.

Keep in mind that anything rated for "12 V" operation intended for end consumers (not engineers that actually understand voltage specs) is most likely designed to work or at least not blow up with 12 V car power.  Even without spikes, that is actually more like 13.6 V when the engine is running, so it is quite likely this buzzer can handle 14 V.

18 V is more of a stretch.  If this is a piezo buzzer (you didn't provide a link), the higher vibration amplitude could damage something.  Eventually the higher power could cause overheating and damage something that way, but that is unlikely to be a problem with infrequent bursts lasting only 2 seconds.

The correct answer is to get a 12 V battery.  Unfortunately those are not as widely available as 9 V batteries.  Another OK answer is to run it from a single 9 V battery.  Try it, it might be loud enough.  You can also do what Coder suggested, although it will use the batteries less efficiently.  Find a resistor so that you end up with about 12 V accross the buzzer.  Put a capacitor accross the buzzer to keep the voltage roughly constant, else you will still exceed the voltage spec some of the time.

Another possible solution is to not worry about bears.  You didn't fill in much in your profile (remember, that's really a courtesy for us, it's not for you).  Your mug shot implies Africa, but there are no bears there.  Maybe you live in place where there are brown bears or polar bears, but if it's just black bears this seems paranoid.