I'm certainly no expert on fifteenth-century naval architecture, but I'm pretty sure I know the answer to this one. The answer is: nobody knows.
The amount of firm information about Columbus's ships is extremely scanty. We have a list of the sails of the Santa Maria (fore course, main course, main topsail, mizzen, spritsail), because Columbus happened to mention it in his journal. ("I allowed them to set all the sails....") We know the Nina started out as a "caravela lateena," with lateen sails on all her masts, and got rerigged in the Canary Islands as a "caravela redonda." The glossary in the relevant volume of the Conway's History of the Ship series (which is where I usually start when looking up such matters) defines "caravela redonda" as "a caravel with square canvas on at least the fore mast. There is an example as early as 1438-39 built by Portuguese shipwrights for Philip the Good of Burgundy and at this time the ships seem to have carried a squre main and lateen mizzen. Later three-masted versions became common, with square fore and main canvas and lateen mizzen; most famous of the latter configuration was Coulumbus' rerigged Nina."
Most reconstructions of the Nina in her initial configuration seem to give her two masts and no bowsprit (though I think I've seen at least one with three masts). It seems likely that in her rerigged configuration she would have had a bowsprit, but I don't think anybody can say for certain.
Youth, talent, hard work, and enthusiasm are no match for old age and treachery.