Intercity bus service to and from Cubatão is provided by several companies. The one that seems to have the most departures every day is Breda, with hourly departures to major terminals in São Paulo on some days.
The bad news is that Breda only serves the Holy Lowlands (Baixidas Santistas) so the farthest you are likely to get is Osasco or Itanhaém.
Cubatão Off The Beaten Path
At the summit of the hill in the center of the Parque Ecologico Cotia Para there is a statue of Christ the Redeemer. The statue was inspired by the one in Rio de Janeiro, but is only a small fraction of the size.
From the view point where this statue is located it is possible to see all the way to Praia Grande, Santos, and Guaruja.