Bathroom fan with no outside vent
IMO, and IME, bathroom fans should always be vented outside. Bathrooms are one of the biggest (if not the biggest) producer or water vapor in your home. When water vapor is trapped is can cause things like mold, mildew, damage to furniture, added difficulty in conditioning the air, and many more.

Just because a bathroom vent is not currently vented to the outside, does not mean it can't ever be. The house I'm currently living in had no ceiling exhaust fan or light (just a vanity light).

In this situation I was able to wire in and install a new unit, with manufacturer recommended vent line and exhaust this line through the closest soffit.

Depending on the layout and positioning of your bathroom, you could run through above joist spaces until you reach a soffit, run into the attic and then out a vent, or simply through the nearest exterior wall. Many times the shortest route is the simplest.

If this is something you aren't comfortable with, I highly suggest finding someone who can like a general contractor, trusted handiman, etc.

Keeping excess moisture out of your home will pay large dividends in the problems you're preventing.