The Specialissimas I've seen, 1960-1965, have chrome bands on seat tube and chrome socks on fork and stays. Serial numbers are 16X XXX on seat lug. For example
Bikeville thoughts: 1960 Bianchi Specialissima
My guess would be a model called "Campione del Mundo", maybe 1960-ish. I've seen some of those (in photos) with no chrome bands or socks.
Might have been refinished at some point, with different decals and badge. I believe that celeste Bianchis were not exported to the US in the early 1960s, but of course bikes can be bought in Italy and privately brought to the US.
But I'm not an expert, I own a Specialissima but no other model of Bianchi.