If it takes ten months for a spammer to point out there’s a zombie in your bathroom … your fan is doing a fine job …
These are experiments I have actually done. Although in my case I am trying to keep shower humidity from raising the RH in the bedroom. My bathroom fan is 100 cfm, pretty standard, with a very short direct route outside.
The best way to keep the bedroom’s RH from rising is to crack the door about 1/2" and place a towel across the opening at the bottom of the door. Then hang a shirt or something on the door handle and stuff it into the lower part of the cracked opening. That opening at the bottom of the door alone in my case is 30" x 3/4" or 22 square inches. A 4" x 5" opening, much more than you might think. By closing off the bottom and the lower part of the side, you force the incoming air to come in at the top. This is best for the steam which is at the ceiling.
After the shower, leave everything like that for a few minutes, then open the door about 6-8" to let a good air flow in but still prevent recirculation to the bedroom. When I am done I still only open the door about halfway while dressing in the bedroom.
You can also open a window instead of cracking the door, but you have to take the outside air as is, and in my case it is usually very humid.
In the winter, I just leave the door open because you can use the humidity in the house.
Dennis