The "I" dimension (height of the jib) on a 38-200 is 50 feet.
Add a foot for the distance between the top of the jib and the top of the mast.
Add the height of the bow above the water (I'm going to guess~5 feet)
....and you're at ~56 feet from water to top of mast. NOT counting anything that extends above the mast
So... I'm going to go with "no", I don't think you're going to make it under a 54-foot bridge.
Easy enough to come up with your own *good* numbers, though. connect the end of a 100' tape measure to your main halyard, raise it to the top of the mast, and then read the tape at the waterline next to the boat. That'll give you a good baseline number, and then add something to reflect the height of things that extend above the masthead. My antenna extends a little over 3 feet above the top of my mast, but I added 6 feet to my air-draft number just to give myself a little bit of breathing room. I'd rather be pleasantly surprised than unpleasantly surprised...
$.02
Bruce