To minimize bird dust from my seven budgies I position a Honeywell air purifier on the floor right next to each cage and run it continuously. I vacuum the pre-filter once a week and the amount of white feather dust it collects is amazing!
I also keep my budgies in 24x24x32 plexiglass "cages" made by Pennzoni Display Company, two budgies per " cage. These cages have 82 pre-drilled holes on the top and sides to hang decor and a three inch diameter hole on the back panel with a built in ventilation fan that draws fresh air in via the holes and vents it out the back. I put a 6" square of the air purifier pre-filter over the fan exit to catch any budgie dust, and it catches A LOT! The acrylic cage panels side together so they are not even close to air tight, allowing even more fresh air to be drawn in via the fan.
The cages are very well made, though expensive and worth it because I have severe asthma.
Between the air purifier running very close by and the cage set up itself very little bird dust escapes into the rest of the room.