Leave the door open when it's not occupied.
If the mini-split faces the bathroom, such a fan might not even be necessary.
See drawing in original post. Will prob put Mini Split on back wall opposite of garage door. Or might put it above bathroom door (depending on space and access).
I would put a wall pass through vent high up in the bathroom wall in front of the toilet. The door should have a gap at the bottom when closed. When the bathroom door is closed and the unit is running, convection will cause the colder air to go under the door and hotter air to be drawn out the vent.

Make the bathroom wall 6' high.......
They do, but you loose a lot of efficiency.They also make ducted mini-splits where you can use small duct work to dump air into other rooms.
They do, but you loose a lot of efficiency.
How do you cool your closet in your bed room?
Tjernlund AireShare Room-To-Room Ventilator
Or similar
https://www.northerntool.com/shop/tools/product_200338939_200338939?utm_source=google_PPC&utm_medium=Dynamic%20Search%20Ads%20Test&utm_campaign=Heaters%20And%20Stoves_DSA_Migration&utm_content=&gclid=CjwKCAjw8-LnBRAyEiwA6eUMGvONBRDM5bz9ZthqtdiUhSDJRhKQWCDLpoiDmFDkxJqWuqpi1n_KIBoCXokQAvD_BwE
It's not a lot. The new ceiling cassette systems are very efficient and a great choice for some applications.
DC
I have a 640 square foot cabin with only a single head mini split.
What size MiniSplit do you have for your cabin?
This looks pretty cool.
I have a utility closet in my basement that houses my boiler and water heater. It's about 10'x15'.
Could I use this to draw heat out of that space into the living space? The room gets very hot in the Winter. My concern would be creating negative pressure in the utility space that might pull CO in from the chimney.
room to room fan facing IN to the bathroom
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If you find yourself sitting in the bathroom long enough that a slight temperature variation caused by your mini split is an issue, I would recommend you start a Citracell or Metamucil regiment.
This looks pretty cool.
I have a utility closet in my basement that houses my boiler and water heater. It's about 10'x15'.
Could I use this to draw heat out of that space into the living space? The room gets very hot in the Winter. My concern would be creating negative pressure in the utility space that might pull CO in from the chimney.
Tjernlund AireShare Room-To-Room Ventilator
Or similar
https://www.northerntool.com/shop/tools/product_200338939_200338939?utm_source=google_PPC&utm_medium=Dynamic%20Search%20Ads%20Test&utm_campaign=Heaters%20And%20Stoves_DSA_Migration&utm_content=&gclid=CjwKCAjw8-LnBRAyEiwA6eUMGvONBRDM5bz9ZthqtdiUhSDJRhKQWCDLpoiDmFDkxJqWuqpi1n_KIBoCXokQAvD_BwE
You are over thinking this...passive cool air will cool enough...
Bath exhaust fan should pull enough air into room when door is closed.
the problem should be covered - lol.
Not in more extreme climates, especially if the bathroom has an exterior southern-facing wall.
Agreed, but we don’t know what Mike’s location is. My SIL has a 30x50 Shop with a non climate controlled bathroom and its not that bad...NC can get pretty hot so we’re familiar with the heat.