This can usually be found on the official MAME website or forums, where developers and community members share necessary files.
This list is not exhaustive, but it covers the most common systems that users would have needed BIOS files for during the 0.139u1 era. mame 0139u1 bios pack
Unlike console emulators (where a Super Nintendo ROM works on basically any SNES emulator ever made), MAME ROMs and BIOS files change over time. As the MAME developers discover cleaner dumps of original arcade chips or better understand how a hardware restriction worked, they update the required file structures within MAME. This can usually be found on the official