The answer for me was windowed mode, using obs (not streamlabs), and capturing the part of the desktop with the game in.
What do you use to capture the game? Streamlabs OBS seems to have an issue with this game. It stopped working after the first loading screen. I've captured Sonic Adventure 2 with no problems.
Ok I figured it out! If anyone else needs help with this in the future, there's quick PowerISO tutorials on youtube. Or you can message me on discord.
I installed the game using the .nrg file that's been put in resources, but now I'm having trouble launching the game on PC. I tried BugsBunny.exe initally and that didn't work at all. Then I used setup.exe and apparently that installed the game properly, so now BugsBunny.exe brings up a launch window, but then when I click play it says "Please insert the Bugs Bunny Lost In Time CD-ROM". I don't know if that would actually work but I only have it on PS1, so I can't try it really. Help would be appreciated if anyone knows what I'm doing wrong, I'd like to speedrun this game.