Not well. Bleeding textures off edges from the "better" bilinear filtering as all playstation textures are rendered from pages, and have had hardlocks. Stopped using Bleem! in 2000 and just left PSX emulation alone until pSX some 2006 later.

Macs apparently had it better with VGS in the day

Bleem! is a piece of history, but it's an early emulator and have compatibility issues.

ePSXe is a better emulator but it uses plugins, so it is not as easy to configure. Go get ePSXe 1.5.0 if you want to play PSX games on Windows 9x.

(P.S.: I think ePSXe doesn't use plugins anymore, but older versions do)

its not great, i tried final fantasy 7 it worked for about 10 mins then i got graphical errors that covered most of the screen making the game unplayable, i also tried out an FPS game called disruptor, it was playable but did have some graphical errors until i changed some options, played a few levels and was pretty cool, its worth trying out just to see how games run on old hardware but i wouldn't actually use it for playing through a game.

epsexe is a better option, though in the 20years its been around ive never managed to get it to work right or look good no matter what plugins i use, there was also a couple of forks i think was called something like pcsx rearmed or reloaded, for me it just looked like the GUI had been updated but the emulation was just as poor as it was 20 years before. thank god for duckstation.

also as leileilol mentioned theres VGS (connectix virtual game station) originally for Mac, theres also a windows version, havent got round to trying it yet so not sure if its any good.