So, this may be controversial but I have come to the conclusion that the Screened bottom board is not that all effective for mite control and is not worth the extra expense and work to use just as a ventilation aid.
For starters, the mites that fall off are usually ones that are injured, sick or just plain unlucky. These represent a small portion of all of the mites in a hive, of which most are in capped cells any how and are not falling out. So the mechanical mite drop is not that effective.
Then we have the issue of medications. If you plan on using medications, many require the bottom to be closed to that the chemical vapours (like thymol) have a chance to fill the hive and kill the mites. So then you need to use the silly flimsy trays supplied to seal them off. The only "medication" I see benefiting from the sbb (if you can call it medication) is powdered sugar, which requires too many applications because it does not get mites in the cells and then I need to buy all of the sugar.
If you want to go treatment free, the issue in my mind is not mites dropping, but rather mite management by much more proactive ipm methods like drone trapping and brood cycle delaying. Better yet are more hygienic bees that can combat the mites by recognizing and removing infected brood. These are not reliant on natural mite drop.
Finally the issue of ventilation:
While I think ventilation is very important in a hive as it controls moisture management, there are other ways to get ventilation other than a huge gaping hole in the bottom of the hive. Popsicle sticks under the top cover for instance or drilling small ventilation holes or using shims all serve the same purpose just as well. (perhaps maybe not in the humid south or bayou areas but at least where I am in the North East) Where I live in New York I find that the winds and cold winters make it impossible to keep the bottom open in the winter, so I need to put the useless-cheap-plastic-election-sign-material-insert in again which has no insulative value. In the summer when its really hot, you could use rocks to prop the telescoping cover up or invest in slatted racks which can stay in the hive permanently.
...So now I am going back to buying solid bottom boards What says the board?