I thought about what you asked, and I'm assuming that you don't have bullets and are thinking about buying 377 bullets (38-55). That's a good place to start, most bullets from casters are hard, BHN 15 > 18, or perhaps more. Ideally a bullet works best if not sized down too much. I had a batch that I cast up for my 38-55, sized to 377, that I gave to a friend to shoot in his 375 H&H. They would not shoot in my 94.
Don't buy too many before you figure out what works best.
There are many factors that come into play for cast bullets. Although I have no experience with cast in the 375 H&H, I do shoot cast in my 38-55.
Actual bore (groove) size needs to be measured in most cases, the grooves may be 376, 377 or ???
Cast bullet hardness comes into play also. If cast of pure lino, BHN 22, groove sized cast bullets work, slightly under ok as well. Softer alloys work better at groove or slightly larger.
One of my bucket list guns is a 375 H&H, I would load them with a gas checked bullet, and my goal would be a 1600 fps load minimum, and up to 2200 fps if possible. With cast, heavier bullets have an advantage, so 250 gr bullets would be the lightest I'd try. In my 38-55, a 270 gr (app) hard cast gas checked bullet works well at 1500 fps. A softer bullet, 285 gr. is good at 1300 fps.
Fortunately there is a lot of good cast bullet data for the 375 H&H.