I am not on the Bitbucket team but will try to help.
Here is the guide for deploying from pipelines to Google Cloud (App Engine) https://confluence.atlassian.com/bitbucket/deploy-to-google-cloud-900820342.html
You will need to substitute some off the google cloud sdk commands with those relevant to firebase: https://cloud.google.com/sdk/gcloud/reference/firebase/
I hope that helps!
We are excited to announce the open beta program for self-hosted runners. Bitbucket Pipelines Runners is available to everyone. Please try it and let us know your feedback. If you have any issue...
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