I agree with the others that upgrading your shop is best. If that was not possible and I needed to put a mini or midi lathe in a bedroom, here’s what I would do.
First I’d build a box for the ac duct with a filter on it to stop dust entering the duct when ac is off.
For the return air duct, I’d include a fan to suck air out of the room, pass it thru a hepa filter, and into the return duct. This would keep dusty air from flowing out. Could be as simple as a box fan with filter taped to it stuck over the return.
Then I would want something to catch as much dust as possible at the lathe. Since the big dc is in garage, I’d think about something like this, reversing it so it sucks instead of blows. Add a hood made from cardboard and set it behind the lathe.
This site is all about dust collection and protection. It shares the risks from fine dust exposure, how to measure your risks and how to effectively protect yourself and those close to you from airborne dust hazards. Fine dust is so extensively studied that researchers call it PM short for...
billpentz.com
I’m considering making one of these for my lathe even tho I have a dust collector. I want something quiet enough to run all the time.