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You are right about the letter B, our B-sound is represented by the letters mp in Greek. This raises a question - how was your ancestor's name written in Greek letters? I have read on the net that there are people of your surname living in Greece today, I don't know if that's true. If it is it should be possible to learn the Greek spelling of your name and so begin the search for its meaning. I can see several possible permutations of letters.
I suggest you seek out a forum that publishes queries about Greek surnames, I'm sure they exist.
There is a Hydra website with a historical article that mentions several local families. Unfortunately there is no name like yours there.
http://www.hydra.com.gr/history/