Banamichi is on the Ruta Rio Sonora, the scenic highway (Mexico 17) that runs the length of the Sonora River valley from Ures in the south to Cananea near the US border.
By car from Hermosillo: Head north on Mexico 14 toward Ures, then pick up Mexico 17 north. Banamichi is about two hours from Hermosillo under normal conditions. The road is paved throughout and in decent shape, though the last stretch through the valley has the occasional pothole.
From the US border: Nogales or Agua Prieta are the usual crossing points. From Nogales, head south on Mexico 15 then east on Mexico 89 toward Cananea, then south on Mexico 17 into the valley — roughly three hours to Banamichi. From Bisbee, Arizona, cross at Agua Prieta and drive south through Moctezuma; the distance is similar.
By bus: There is no direct bus service to Banamichi. The nearest regional hub is Moctezuma, about 25 km east, which has connections to Hermosillo. From Moctezuma you would need a taxi or to arrange a lift.
A car is effectively required. Public transport to the valley is minimal, and distances between the river towns mean there is no realistic way to get around without your own wheels.