If you are searching for an ancestor’s origins before 1811, it might be worthwhile to check the town registers to see if they submitted a bond letter. This is a certificate given out by their previous place of settlement that indemnifies the new town in case the person becomes poor. The old place of settlement promises to support them. If you find a bond letter, this will tell you where they came from.
Is the surname Labisonniere a Dutch surname? Could it have been shortened to Labis?? or is it someone from a possible French or Flemish town Buisson [bush in English?]??
That name sounds French rather than Dutch. French people did emigrate to the Netherlands so it’s possible. The only way to find out is to research the people back in time.