Need better photos to be sure of much. First hub photo it does look like a Tipo. Later photos show 3 piece hubs, which could be correct. Looks like closed C on shift levers which is later. The alloy seat post is later. Looks like 60s Fiamme Reds. I'm thinking this is 1963 or 1964 unless someone did a good bit of re-equipping. Is the paint original? Decals? Where is Bianchi Girl? Even if it is a repaint and rebuild it is still a rare and desirable bike fairly well presented.
$2000? Not for me. Someone might. Would make a great rider if it is not good enough to be museum.