Well, its been so rainy here in NYC the last few weeks the girls don't have to go too far to get to standing water. Its sitting right on their roof.
If you don't want to use Mosquito dunks, how about a couple of goldfish or cheap feeder fish like guppies in the bucket -- if its a 5 gallon bucket it could hold 2 small goldfish without a problem. As long as the water isn't standing in the open sun all day it shouldn't get too warm and the O2 level should be ok for the fish. They will eat the larvae. I have two goldfish in the (very) small water pond in the back yard and it works well. The birdfeeder gets dumped bi-weekly or the larvae get too numerous. The girls like to visit both.