Bilwi is in Caribbean Nicaragua.
"Bilwi" is the indigenous name of the town which was renamed "Puerto Cabezas" after some general or such during a time when the central government in Managua didn't even pretend to care about Nicaragua's indigenous people. In a move similar to Stroke County in Northern Ireland, the compromise between the two names implemented later on is that the town itself is officially called "Bilwi" while the municipality is called "Puerto Cabezas".
The overland trip is lengthy and difficult. The roads are in a bad state and the lengthy rainy season in the East of Nicaragua does them no favors. The road unpaved most of the way and even the official times (which are over 20 hours one way) can be an underestimate due poor weather and breakdowns (the old school buses from the USA that ply this route are known to break down often). On the plus side, the ride is cheap and the "real Nicaragua" doesn't get much more "real" than this.
If you want to attempt to get a car from the West of Nicaragua to Bilwi, you should be prepared to have to dig out stuck tires, find some way around if a bridge over one of the many creeks isn't in working order and of course you should only do this trip in a four wheel drive. Having a local driver is certainly a plus, but not all drivers will be willing to do the trip and not all rental car agencies will let you take their cars there. Locals do not necessarily speak English or Spanish along the way, which poses further complications. When in doubt ask for a "cacique" who is usually a respected local authority (if the "alcalde" [mayor] isn't the same person, their authority is often nominal at best) and likely speaks Spanish.
True, Bilwi does have a dock and its Spanish name even contains the word "Puerto" and there are indeed freighters and fishing boats that visit this port quite regularly, but there is no scheduled passenger service, unfortunately. Freighter travel might be an option if you know whom to ask. The website (dead link: January 2023) of the national port administration (EPN) gives a bit of information, including on the prices of certain services (Spanish only). Unfortunately, the Website of EPN is known to contain outdated information at times.
Primary administrative division