Well, hate to tell you this, but in my opinion late March is perhaps the single worst time of the year to be dealing with going outside around Hatteras... I'd sooner be out there in late January, as a rule...

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The reason being, that's the time of the year where many of those systems that originate in places like Arkansas, and intensify while moving across the SE, producing tornadoes and violent weather, draw a bead on Hatteras. If they happpen to meet up with a late winter cold front, watch out... I think more boats get into trouble out there in the late winter/early spring than any other time of the year, one reason being that sort of weather is notoriously more difficult to predict than the more typical march of cold fronts across the region in late fall/early winter...
Having said that, however, given the amount of time you seem to be allowing yourself, it certainly is do-able. All of my trips outside in the early spring have turned out to be pretty tame, in the end... You simply have to be really,
REALLY cautious when it comes to the weather...
Departing from Beaufort, of course, gives you a big advantage, you can sprint up to the Bay Entrance in pretty short order. You definitely want to have the capability to motor all the way, that's not the time or place to be dawdling around in light air, you want that leg over as quickly as possible. As Yorksailor says, stay inside the Stream, just go right around the red nun "2" right off Diamond Shoals, and up the beach to the Bay... If you happen to luck out with a SW breeze, that can be an absolutely wonderful sail, and that time of the year seems to be a good chance of seeing whales in that area...
Another thing you might consider, is simply moving the boat elsewhere in the area south of the bridge - to the Beaufort Docks, or over to Morehead City waterfront - and wait until later in the spring or early summer to move her north...
Bottom line, I'm not trying to dissuade you from making the trip, but simply suggesting that it can be an extremely volatile time of the year in that area, weatherwise...