My boat is in a marina just across the river from Oriental, and I have sailed under that bridge many times aboard my CD25. Yes, it is a nominal 45 footer, and only in extreme flood conditions would it clear less than 40 feet, so you are safe in your 25D. We don't have solar tides on the Neuse River, just wind tides - water is high with north winds, low with south winds.
The entrance to Oriental Harbor is well-marked and protected, and there are no currents or tides to contend with inside the breakwater. Immediately upstream of the bridge the creek forks, with Greens Creek to port and Smith Creek to Starboard. Greens Creek is a bit wider and less developed along the banks, and you can follow it a mile or more upstream and anchor in sheltered water. The depths run seven feet or more in the channel but shoal rapidly out of it. Kershaw Creek branches off to the starboard but is shallow. Smith Creek is fairly narrow, developed along the banks, and tends to be crowded with anchored boats.
There are several local marinas, below the bridge, above the bridge on Smith Creek, and on Whittaker Creek which is the next creek down the river from Greens Creek.
My experience is that hurricanes this far north tend to lose a lot of punch as they come over the shoreline. Oriental is a good 10 miles in from the coast, so while a hurricane can bring lots of wind and very high water, it probably won't have the devastating strength of one to the south. The creeks have deep mud bottoms and the hurricane drill is to anchor far up a creek with a Fortress on a length of cable. This combination digs far down into the mud and makes for a solid hook-up.
I'll put in a plug for my website,
http://www.neuseriversailors.com, as a good source of information for anyone considering sailing the Neuse River or Pamlico Sound.