the buses display the sign 'niterói/charitas' and are operated by the two companies auto viação 1001 and braso lisboa.  both lines follow an identical route.  detailed bus itineraries for the two bus lines can be seen here and here. 

there is no bus service that gets to the entrance to the parque da cidade, so the only option would be a walk from the bus stop near praça rádio amador,  or a 10 minute taxi ride. 

if hiking, the walk is quite steep and would take about 30 minutes - proper shoes and a bottle of water are highly recommended.