I would recommend installing a bath fan with a new vent that goes to the gable wall roof or even the soffit last choice.
How to vent a bath fan through the roof.
You may just want to go with a completely new vent the whole way most modern bathroom fans require 4 or 6 vent hoses for much better performance and lower noise.
I recommend that my clients vent their bath fans out a gable wall if at all possible when not using an hrv or erv that is.
It eliminates the need for routing ductwork through the house and these fans usually dry the bathroom more quickly.
If you vent through the roof condensation will drip back into the interior.
The best exhaust fan venting is through smooth rigid ducts with taped joints and screwed to a special vent hood.
Venting through a roof vent or exhausting them in the attic could cause moisture problems and rot.
This involves running ductwork from the fan usually though an attic and out through the roof.
The 2nd bathroom vent drips on the floor and is ruining the ceiling.
Depending on the location of the bathroom it may be easy to vent the exhaust fan through the roof.
A down through soffit exhaust vent design by leaving warm air in the exhaust duct when the fan is off creates a heat trap that reduces heat loss out of the bathroom through the exhaust fan duct when the fan is off in comparison with up routed vents or even horizontal vents through a gable end wall.
This article describes routing bath exhaust fan duct upwards through an attic or roof space or downwards through a floor or crawl space.
Next use aviation snips to cut slits into the sheet metal sleeve.
The 2 pipes one a 4 master and the other a 3 2nd do not go through the ceiling but into a common box that goes through the roof.
Pass the opposite end of the duct through the hole in roof.
Bathroom ventilation fan duct routing routing a bath vent duct down out or up through an attic or roof out.
Vent your bath and kitchen exhaust fans through the roof through a special roof hood.
In all cases the ducting needs to conduct the exchaust to the building exterior and needs to terminate in an animal proof vent cover.
Run a thick bead of tri polymer sealant along the underside of vent hood.
If you vent through a soffit where attic vents are often located the moisture will get sucked back up into the attic or roof venting.