No Dust Tile Demolition - Tile Coach Video
I just want to give a shout-out to @Isaac Ostrom and his video on No Dust Tile Demolition video on YouTube. I wish I had seen this before demo'ing our first bathroom, which created an enormous amount of dust. Midway through that bathroom, I bought it as we did some drywall work and light sanding.
On to the next bath, which demo started the other day, I popped the fan in the window, turned on high, let the fan hold the filter in place, and let it run as I started to cut out the old tile. What a dream! This works great. There is still a lot of dust, but the air is cleaner, there is less surface dust, and the dust is not drifting out into the rest of the house. Mainly, it is capturing the lighter/smaller particles and filtering and sweeping them outside. The screen in the window already has a halo of dust where the fan faces, haha.
My setup was a simple $25 box fan from Lowes and a 3-pack of 20x20 filters for $14. $39, well spent. Also, my DW likes the fan while she's working on her stuff. Here is the video:


Yes it works great! Glad it helped