If you haven't already done so, you might want to go the the Sticky Thread in this section (Cruising) of the forums and have a look at the Pilot Chart for Feb/March for the Gulf. You'll see that it confirms what PBzeer said above about the prevailing winds (>60% frequency of E & SE winds averaging Force 4), but it also indicates a significant west flowing current off Yucatan that should be considered in routing decsions. The rhumb line is over 800 miles, which is a long distance when going to weather. How well does your cat sail to windward?
If you are committed to a direct crossing, I would suggest that you start looking at the weather charts available on the following NOAA site http://weather.noaa.gov/fax/gulflatest.shtml#WIND
Watch them daily over the month or so before you're planning to leave and you'll get a good sense of the weather pattern you're looking for. With the right winds it should take less than a week in a 50' cat. The 24/36/72 hour surface analysis and wind/wave forecast charts provide a look at what you might encounter over a 3 day period.
Longer range forecasts of offshore winds are available on this US Navy website
(if this link doesn't work Google "US Navy Weather" and look for "FNMOC Welcome Page" which will take you to the right place.)
Windows will probably give you a warning about the lack of a site certificate or something, don't worry about it. You trust the government, don't you?
Under the section "Public Products" click on "Global Wx Prediction Charts"
Then click on "Tropical Atlantic NGP",
When the list comes up look for "Surface Strmlns & wind speeds" and click on the "All" on the far left of that line.
Give it a minute to load and you can scroll down through 7 days of wind direction and speed forecasts. You can also look at "Tropical Atlantic GFS" for the output of a different weather model.
One of the keys to a comfortable and fun sail across will be being able to wait for the right weather pattern to emerge (and being ready to go when it does develop). If you have a schedule to keep, you'll have to take whatever NOAA has on the menu for the week after you leave.