Brass is generally not hard to get. You can do what mooncoon says, or use 375 Winchester brass, which is also a bit short, but works fine.
Bullets can be a bit more tricky. Most 38-55 rifles do not have .375 groove diameters, but closer to .377, with some as large as .379, even with newer built rifles.
This means that Hornady's 220 grainer designed for the 375 Winchester does not work in some rifles. [mine is one of these]
Barnes makes an excellent 255 grain softpoint specifically made for these larger bored 38-55 rifles, it is sized at .377", and shoots exceptionally well in my rifle. However, they are not always easy to get, and they are pricey. [Part # is 38/5520]
A good route is cast, and there are plenty of good cast FP bullets around for the 38-55, sized at anywhere from .3775" to .380" I love these bullets, and shoot them a lot. You can drive a gas-checked 285 grain bullet to 1700 FPS in a M94 built more recently, and it will kill any deer, moose, elk, etc that you shoot it at. Mine shoots this type of cast into less than 2" at 100 yards. There are several other cast offerings available in weights from 240 grains and up that work well in the 38-55. Use H322 or IMR 3031, RL7, IMR 4198...all's good. Regards, Eagleye.