It depends how wide your bowl is. If you have a container just as narrow as it's outer diameter, it's going to run out fast while if it is sitting in a wide body of water, it'll last much longer.
I'm assuming you can run it for prolonged periods of time since it sits in water. Mine says 10hrs continuous but that's a lot of water it'll atomize. If you do run it for long periods of time with regular water, you'll have to dip the little disk in CLR or something every once in a while as it'll build up with minerals. It should give you a small spanner wrench with the atomizer to access the part. Also the body of water gets pretty warm...perhaps dangerously warm after a while.
The main problem when I ran mine a while ago is the fogger spits up a "cone" of water from the surface. Mine is sitting in a container about 4" diameter so this water would constantly splash out and around on everything else and in effect made my container run out of water fast I solved this by rigging an inverted "cone umbrella" right above the surface where the water cone spits up. The water will cling on this and drip back into my small container and make it last longer.