In case you run into issues using turborepo and bun, this a quick workaround.The problem:

Turbo error: error preparing engine: Could not find "___ROOT___#build" in root turbo.json

Just put following line into your package.json. This will make npm write a lockfile, that is needed by turborepo.
Run bun install afterwards.

...
  "scripts": {
    "postinstall": "npm install --package-lock-only --ignore-scripts",
...