This week's book giveaways are in the iOS and Features new in Java 8 forums. We're giving away four copies each of Barcodes with iOS: Bringing together the digital and physical worlds and Core Java for the Impatient and have the authors on-line! See this thread and this one for details.
You already have SCJP and SCWCD, so you know how these exams work. SCBCD is not much different. I'd say four weeks should be enough if you are determined, even less if you know something about the subject.
Of course Hebert has the point here: only you and mocks can tell how close you are to achieving the goal.