Bernardsville is the only New York suburb I can think of that
has 13 letters.
But if you're looking for "places in New York" beginning with
"B" for a competition then the most obvious choice would be
Bloomingdales. It's not a suburb but it is a place in New York.
Oh yes, and there is a suburb called Bloomingdale (without the
s) but that's only 12 letters.
Regards,
NigeC.