I use Bun in CI too, and they have a clean GitHub Action for it:
https://github.com/oven-sh/setup-bun.
Actually now that you mention CI, I remember now that I did also run into non-deterministic problems running type checks on projects with Bun using Github's free runner.
Errors looked like this, but it worked fine every 2/3 runs with the exact same code:
`tsconfig.json(5,25): error TS6046: Argument for '--moduleResolution' option must be: 'node', 'classic'.`
It was fixed by just running on my own runners instead, and I never hit those errors building locally. Very weird.