Rio de Janeiro is well served by buses. There are many lines in the region of CBPF coming from Copacabana, Ipanema, Botafogo, Flamengo or Catete. The same happens with Casa Rui Barbosa, but it is also served by the line 1 subway, and it is 200 m from the station Botafogo. Line 1 connects all these 5 neighborhoods.
The one-way ticket both for buses and subway costs around one dollar.
Taxis are very easy to find in Rio. You can take them on their stations or directly on the streets. The fare starts at R$ 5.40 (around US$ 1.50) and the kilometer is around R$ 2.30 (around 60 cents) in week days, from 6 am to 9 pm, and R$ 2.76 (around 70 cents) on weekends and from 9 pm to 6 am. You can find more information on the site http://www.tripadvisor.com/Travel-g303506-s304/Rio-De-Janeiro:Brazil:Taxis.And.Rental.Cars.html