I'm a big fan of the .38-55 and got into it through the back door via the .375 Winchester.
The .38-55 has more than its share of quirks and the .375 Win contributed to those quirks.
Bore Diameter:
As noted above there is a lot of variation in .38-55 bores. They'll range all the way from .377-.379" in a modern .38-55 to .381" to .383" in a vintage .38-55.
Jacketed bullets are generally found in .375" diameter only, and of those, .375" bullets suitable for the .38-55 or .375 Win in terms of weight, point shape and core alloy hardness (for expansion) are pretty scarce and run from "very hard to find" to "unobtainable".
Fortunately, cast bullets can normally be found in .377", .379", .380" and .381" diameters and in a variety of suitable weights, and in both plain base and gas checked varieties.
Brass Length:
.38-55 brass comes in two basic lengths. The original 2.125" .38-55 case and the modern 2.080" case used by Winchester since the .38-55 was resurrected. There's a reason for this.
When Winchester introduced the .375 Win in 1978 it was basically a .38-55 operating at a much higher pressure - 52,000 CUP versus 30,000 CUP for the 38-55. Rather than using a longer case (like the .357 Mag versus .38 Special) to prevent the .375 Win from being chambered in a .38-55, Winchester took a different approach. They instead used a true .375" diameter bullet in the .375 Win and used a slightly shorter case length of 2.020".
This approach ensured that if a .375 Win were fired in a .38-55, the undersized bullet would pass through the bore with minimum pressure, and the shorter case would have ample room to release the bullet even in a "tight" .38-55 chamber.
Conversely, Winchester also designed the .375 Win chamber with a long leade and large throat diameter that would enable a .38-55 cartridge with the modern .377" standard jacketed bullet diameter to release the bullet in the .375 Win chamber. The bullet would get sized to the .375" bore, but the max pressure for the ,375 Win would not be exceeded.
The end result is .38-55 brass in two lengths - the original 2 1/8", expressed today as 2.125" and the shorter modern case at 2.080". Then there is the .375 Win case at 2.020".
The shorter length also had some production benefit for Winchester as they could use the same basic case to make the .38-55 that they used for the .30-30, omitting the additional step of necking it down to form .30-30 brass. The 2.125" case can't be formed without wasting a lot of excess brass that has to be trimmed from the 30-30 case, and .30-30 is produced in massive numbers compared to the niche .38-55.
Starline does runs of .38-55 brass in both lengths. Starline also makes high quality .375 Win brass from time to time and it's worth picking up when it's available. The alternative is to fireform it from .30-30 Win brass, and the end result has slightly thinner case walls as it's designed for the .30-30 pressures. If you're in a .38-55 brass drought, .30-30 brass can be blown out to .38-55 as well, with the qualifier that it comes up a bit short of the 2.080" length.
The process I've used for form .30-30 brass in either the .375 or .38-55 chamber is 9 grains of unique loaded in the case with the case them filled to the base of the neck with cream of wheat. A pea sized wad of toilet paper is then inserted in the neck to hold the load in place. When fired vertically, the result is a slightly short .375 or .38-55 case with a nice even case mouth. (If you fire it horizontally, the case mouth will be lopsided and need more trimming to true up, further shortening the case.)
As it is, I buy both .38-55 and .375 win brass from Starline 500 at a time.
Case Wall Thickness:
Case wall thickness also varies. Winchester .38-55 brass has a thicker neck designed for the .3775" jacketed bullets they use in their factory load. If you try inserting a .380" to 382" in bullet in a Winchester case, you can encounter problems with the chamber be too tight to accept the completed round, or not have quite enough room to expand and release the bullet when fired without excessive pressure.
The Starline brass has a thinner .0072" wall thickness at the case mouth and works well with cast bullets.
Rifling Twist:
Rifling twists in .38-55 vary from 1-20" to 1-18" in older .38-55s to 1-16" to 1-14" twist in newer .38-55s. Mine Winchester LF in .38-55 measures at 1 in 15" and gives excellent accuracy with flat based 245-250 grain bullets loaded with Unique at black powder velocities.
Generally speaking for cast bullets you want a slower twist to minimize fouling issues, especially if you use black powder, but you also need enough twist to stabilize a long bullet like a .325 grain flat nose, if you go that route.
My Winchester BB 94 in .375 Win has a faster 1-12 twist and it can be problematic with cast bullets - we'll get into that a bit deeper in a minute.
Selecting Bullet Diameter for the .38-55:
Someone mentioned that case bullets are usually more accurate when they are .001" to .002" over bore diameter. That's a general rule for all cast bullet shooting, but you also need to consider the chamber and throat dimensions with the .38-55 and especially with the .375 Win.
Remember that large chamber and long throat Winchester used for the .375 Win that would accommodate a .38-55 round? That extra wide and long throat will cause big problems with cast bullets if you are sizing them for the bore, rather than the throat.
What happens is a lot of gas goes past that undersized (for the throat) bullet and gas cutting removes lead and deposits it further up in the barrel.
In addition, that bullet is now traveling pretty fast when it encounters the rifling at the end of that long throat and with any alloy soft enough to obturate properly, the bullet will skid in the rifling a bit before it starts to spin and that causes serious leading in the first portion of the bore.
You may see that to a lesser extent in a modern .38-55 with a .377" bore, where the chamber and throat are still large enough to accomodate a larger diameter cast bullet. Just go ahead and use the larger bullet diameter, using due caution to work the load up accordingly, understanding pressures may be higher.
You might lose a little accuracy if you are more than .002" over groove diameter - but you'll lose a lot less accuracy than you would otherwise to gas cutting and leading with a bullet that is too small for the throat.
Alloy Hardness:
Some shooters assume that "faster" means a harder alloy is needed. That's not quite the case.
The alloy hardness needs to match the pressure of the load. The alloy needs to be soft enough to obturate quickly in the bore and prevent excessive gas cutting, particularly with a plain base cast bullet.
In the .38-55 there's never a need for anything harder than Lyman No 2 (BHN=15), and a 20-1 lead to tin mix (BHN=10) works well at black powder pressures or low pressure smokeless loads duplicating black powder velocities.
When I could find pure plumbers lead, I'd reserve it for 1-20 alloy.
With wheel weights readily available, I'd use 9 pounds of wheel weights and 1 pound of 50/50 bar solder to create an alloy very close to Lyman No 2.
If I planned to hunt with my .38-55 or .45-70, I went with the 1-20 alloy for the improved expansion and less risk of fragmentation at black powder era velocities.
For the .375 Win, I'll use a 280 grain gas checked bullet and use the Lyman No 2 equivalent.