Well, for ventilation, screened bottoms or slotted bottoms won't be any good unless you have ventilation up top as well. This will create a draft. While looking into ventilation for my roof at the GAF website, they said that one must have the right balance of intake and outflow vents for drafting to work at maximum. Stands to reason since air follows fluid-dynamics principles.
Perhaps a slotted bottom board, a gable-type roof/cover and ridge ventilation would be somewhat ideal. Reasons:
a. a slotted bottom board would provide ventilation across the entire surface area of the bottom. Rather than screening, it would be wood and, therefore, stronger material.
b. the gable-type roof would force the air to vent from the center of the hive, thereby allowing the hot air to collect at the top in a holding space. When the wind moves over the surface are of the peak you get an increased drafting effect due to the differential high/low pressure across the peak.
This is the principle at work in your ridge-vents on your house roof.