99% of PSP games run flawlessly on PPSSPP without any BIOS file.
Unlike many other emulators (like PCSX2 for PlayStation 2), PPSSPP has a built-in, high-level emulator (HLE) for the PSP's kernel and audio. This means you can play most games immediately after installing the emulator without needing to track down or dump system files.
The "PPSSPP BIOS" is largely a myth born from the habits of other emulation communities.