Biome is distributed as a standalone portable binary for various platforms. Initial installation is as simple as downloading that binary and installing in your path.
Download the latest release from the Github Releases Page for your platform.
Example (MacOS):
# Download the binary
$ wget https://github.com/biome-sh/biome/releases/download/bio-0.83.0/bio-0.83.0-x86_64-darwin
# Rename to 'bio'
$ mv bio-0.83.0-x86_64-darwin /usr/local/bin/bio
$ chmod +x /usr/local/bin/bio
You can now run bio:
$ bio --version
bio 0.83.0