Easy to get cast bullets of .380 - .382", but jacketed are much harder.
I have had quite a bit to do with the 38-55, and even the .380" groove rifles have always shot the Barnes
.377" jacketed bullet well.
It weighs in at the original 255 grains, and is specifically designed for the 38-55, using 38-55 cases.
Be careful!! Barnes also makes a 255 grain bullet designed for the 375 Winchester.
It is only .375" in diameter, and as such, usually delivers mediocre performance in rifles with grrove diameters larger than .378" or so.
The other solution would be to get a "bump-up" die and make those .377" bullets "fatter" so they match the groove diameter better.
However, I would try the .377" bullet as is first.
Regards, Eagleye.