Currently, there is no way to disable the email notifications in Bitbucket from a start up / system property, as you can do in Confluence and in Jira.

-Datlassian.mail.senddisabled=true -Datlassian.mail.fetchdisabled=true -Datlassian.mail.popdisabled=true

This is very helpful when mirroring a production environment to a development server.