You can get precast HB bullets from either River Junction Trade or Buffalo Arms. Kind of pricey, but they do have a BP friendly lube and you can get loaded 38 Colt ammo from both of these sources too if you wanted to try them out. River Junction's is loaded with smokeless, and buffalo uses good ol' BP as a propellent.
If you use these bullets, you'll need to load them in the 38 'Long' Colt case as the OAL would be too long with a 38SPl case.
You can also use the swagewd 148gr HBWC bullets from Hornady or Speer, and either smokeless or, if you want smoke and boom, Hodgdon's 777 or APP powder as they really don't require a BP lube. That would save you from having to use a cookie. An you could develop a load using either case, though you'll be downloading the 38SPL to approximately 38Colt ballistics due to having to seat the bullet a bit deeper, though you really don't have to seat it fully as is common in a target wadcutter load.
At fairly close CAS distances, a standard bullet will likely hit the target, but it will tumble, so it's best to go with a HB one for the .375 barrel.
Hope this helps some.