It appears that the CLI doesn't support configuration (e.g. username+password or API token) using environment variables. My use case is direnv, as I use it to conditionally configure my environment rather than relying on global/centralized config when possible. Examples of possible env variables:
BUGZILLA_HOST - sets the host for bugzilla commands to interface with, e.g. BUGZILLA_HOST="https://bugzilla.redhat.com"
BUGZILLA_USERNAME - sets the username to be used when authenticating
BUGZILLA_PASSWORD - sets the password to be used when authenticating
BUGZILLA_API_TOKEN - sets the API token to be used when making an API request
If this is something you'd be interested in supporting, I'm happy to work on this and submit a PR :)