The only things you should be burning would be specifically diseased materials where composting them could perpetuate disease. Otherwise, don't burn the materials, period. Grass clippings make a wonderful mulch and compost easily, for instance. Leaves turn into leaf mold, one of the nicest materials you can introduce your garden to.
Using a bucket to burn in does not increase safety significantly on a windy day, as embers and lightweight burning material can be blown out of the bucket by wind passing over the top and start fires. A bucket is also not a particularly effective combustor as there is only one way for oxygen (air) to get into it - through the open top.
If, and only if, you have a mass of diseased plant material to dispose of and for some reason (what, I can't imagine) needed to do so on a windy day without simply waiting for a non-windy day, then you would need a stove or incinerator with screening to contain sparks, (also known as a "spark arrestor" on the exhaust side, but you need to contain sparks from the intake side as well) so the materials could be burned without the possibility of sparks, embers or entire flaming bits of material being picked up by the wind (or sucked/blown out the stove-pipe) and causing a fire elsewhere.
And indeed, in many cases the local authorities will take a dim view of ANY burning on a windy day, and un-needed burning on any day.