I was told years ago, it may have changed since then, that bug zappers will not work on mosquitoes because they are not light attracted. I had one too for that reason, my son was very allergic to them. But it didn't help, and I started asking around about them.
Maybe they have improved them some now.
Becky
Well, there is also those ultra-sonic thingies. I'm told they are very effective. I used a small plug in one in my kitchen last year and didn't see any bugs in there all summer, except for a couple of flies. I don't know if they would effect the birds outdoors though. It'd be something to look into.