If you REALLY want to be.....
If you REALLY want to be original, a good guess would be a caseload of Black powder.
Here are some points in time:
During World War II, some U.S. aircrew (primarily Navy and Marine Corps) were issued .38 Special S&W Victory revolvers as sidearms in the event of a forced landing. In May 1943, a new .38 Special cartridge with a 158 grains (10.2 g), full-steel-jacketed, copper flash-coated bullet meeting the requirements of the rules of land warfare was developed at Springfield Armory and adopted for the Smith & Wesson revolvers.[18] The new military .38 Special loading propelled its 158 grains (10.2 g) bullet at a standard 850 ft/s (260 m/s) from a 4-inch (100 mm) revolver barrel.
Around 1961 a request for more powerful .38 Special ammunition for use by Air Police and security personnel resulted in the Caliber .38 Special, Ball, PGU-12/B High Velocity cartridge.[21] Issued only by the U.S. Air Force, the PGU-12/B had a greatly increased maximum allowable pressure rating of 20,000 psi, sufficient to propel a 130-grain FMJ bullet at 1,125 ft/s (343 m/s) from a solid 6-inch (150 mm) test barrel, and about 950–980 ft/s from a 4-inch (100 mm) revolver barrel.[2
"In 1956, the U.S. Air Force adopted the Cartridge, Caliber .38, Ball M41, a military variant of the .38 Special cartridge designed to conform to the rules of land warfare. The original .38 M41 ball cartridge used a 130-grain full-metal-jacketed bullet, and was loaded to an average pressure of only 13,000 pounds per square inch (90 MPa), giving a muzzle velocity of approximately 725 ft/s (221 m/s) from a 4-inch (100 mm) barrel"
I don't think factory loads EVER used Bullseye as we know it in cannister powder but - The transition to smokeless powder was rapid and the Special quickly built a reputation as an exceptionally accurate cartridge. It was soon dominating centerfire pistol matches and was widely adopted by police agencies. Not until the 1980's did service autoloaders seriously challenge the popularity of the .38 revolver for police use in the U.S.
For match shooting, a 148 grain lead wadcutter bullet at about 700 fps became the load of choice. Factory loaded match ammunition is offered by Remington, Winchester and Federal, among others. Reloaders typically use a very light charge of an extremely fast burning powder for target loads, such as 2.8 grains of Bullseye, behind a hollow base wadcutter bullet. These are the minimum power .38 loads that most shooters find useful. They are a mild and exceptionally accurate choice for target shooting and plinking.