It only took two months if the weather was very nasty. That number comes from Christopher Columbus' first voyage to the New World, which took 78 days if you count from when he sailed from Palos (August 3rd 1492) to when he landed in Guanahani (October 12th 1492). However, this figure is extremely misleading, because it doesn't take into account the fact that Columbus stayed in the Canary islands for 33 days repairing the ships, getting supplies and having an affair with the widoow of Hernán Peraza.
Gonzalo Fernández de Oviedo, in his Historia General y natural de las Indias, book II, chapter V*, tells us this:
In the name of Jesus he deployed the sails and went away from the port of Palos via the Saltés river to the Ocean Sea, with three armed caravels, starting this first journey, friday August the 3rd of the year of our Savoiur of 1492. [...] As the three caravels were sailing, they went their way to the Canary Islands, called Fortunate by the ancients. [...]
And there, as it was an appropriate place and very adequate for navigation, Columbus arrived, continuing his discovery of the Indies with the three caravels I have mentioned, and there he took water, meat, wood, and fish, and other refreshments that he deemed convenient for his journey. He left La Gomera on September the 6th of that same year of 1492.

This is, of course, the first journey, when he was venturing into the unknown. When the Ocean Sea became more known and people learnt how convenient the Canary Current was, the journey time was incredibly reduced, even in Columbus own lifetime.
Columbus last voyage to the Indies, started in 1502, did not take a lot of time for getting to the Indies, in this case arriving to Martinique. I quote from Columbus' own letter/report:
From Cádiz I went to the Canary islands in four days. From there I went to the islands called the Indies in sixteen days
Sources:
Fernández de Oviedo, Gonzalo, Historia General y Natural de las Indias, edition by Juan Pérez de Tudela, Madrid: Atlas, 1959.
Columbus, Christopher, Copia della lettera per Columbo mandata ali Serenissimi Re et Regina di Spagna, de le insule et luoghi per luit trovate, translation into Venetian dialect by Costanzio Bayuera, Brescia: Simone de Lovere, 1505.