This is going to be a short post, as the 1899 Bergmann is the most difficult variant to find information on. In fact, the 1899 designation is really a catch-all for the experimental pistols Bergmann tinkered with between the 1897 No.5 design and Schmeisser’s invention of a new locking block mechanism in 1901. According to Ed Buffaloe, this series of experimental guns eventually led to the Simplex pocket pistol, although it seems more likely that the Simplex was a separate line of thought and the 1899 was yet another attempt to garner military interest.
We do know that the British government expressed an interest in the Bergmann pistol in 1900, but they did not actually acquire and test any examples until 1902. Whether those test pistols (which were in 9mm, 10mm, and 11.35mm cartridges) were late iterations of the 1897/1899 or early versions of the 1903 Bergmann-Mars is unclear. The most likely story seems to be that the first two British pistols were side-locking 1897 designs in 9mm and 10mm, and they were rejected for using small projectiles (the British military was adamant about maintaining a .455 bore). The followup pistol sent for British trials was in 11.35x23mm, and was likely an early 1903 model with the new locking system.
The pistol was also tested by the Swiss in 1900, who seem to have taken a crack at anything that came out of the Bergmann factory. It once against came up short in their estimation, though (spoiler; Switzerland never did adopt a Bergmann pistol).