Aeolia Schenberg's wealth was said to have completely vanished after his death, so it seems that over the years CB has been developing on the strength of his fortune. Maybe the fortunes of others too, who knows. I have to admit though, I never stopped to think about who could be managing the whole thing. When they need to buy supplies, who decides what to spend and how?
Sumeragi isn't the captain, but since she makes the strategy it seems understood that the rest of the crew is supposed to follow her orders. Not that this stopped Tieria from talking smack, of course.