Using gcloud run services describe on the cloud run service name got it. I was able to use something like this in my cloud build script:
SERVICE_URL=$(gcloud run services describe $CLOUD_RUN_SERVICE_NAME \
--project $PROJECT_ID \
--region $CLOUD_RUN_RUN_LOCATION \
--format "value(status.url)")
echo $SERVICE_URL
Where $CLOUD_RUN_SERVICE_NAME is the cloud service name, project ID the project ID it is running in, $CLOUD_RUN_RUN_LOCATION the location it was deployed (e.g. us-west1). --format "value(status.url)" returns the URL of the service for use in other steps!
The forum wouldn't let me use double "$" but if you use that in a cloudbuild.yaml you'll need to double "$" every variable except $PROJECT_ID, and pre-load the variables as environment variables.