Can I vent a stove hood and bathroom fan through the same duct?
Code says no, because you don't want to wind up with a greasy disaster on your hands later
Section M1503.3 of the 2018 IRC puts the kibosh on your duct-sharing plan:

M1503.3 Exhaust discharge.
Domestic cooking exhaust equipment shall discharge to the outdoors via a duct.  The duct shall have a smooth interior surface, shall be airtight, shall be equipped with a backdraft damper and shall be independent of all other exhaust systems.  Ducts serving domestic cooking exhaust equipment shall not terminate in an attic or crawl space or areas inside the building.
Exception: Where installed according to the manufacturer's instructions, and where mechanical or natural ventilation is otherwise provided, listed and labeled ductless range hoods shall not be required to discharge to the outdoors.

The reasoning for this has to do with the one thing that every range hood on the planet inhales: grease vapors.  While hoods in commercial service get far greasier than their residential counterparts, even a residential hood inhales enough grease that some will condense out onto the inside of the duct and make a mess there.  Even before you get to the obvious problem of a grease fire in your range hood spreading to the bathroom via the shared duct, you'd find yourself with an IAQ nightmare on your hands with cooking odors and stale, greasy smells getting into the bathroom via leakage in the non-return flappers.
And this is before you get to the IAQ nightmare that is bad bath odors invading the kitchen!