After successfully cloning my repo from heroku and added another remote
1/ git clone git@heroku.com:[APP].git
2/ git remote add bitbucket ssh://git@bitbucket
Deployment keys are read only. To enable write access you need to:
Remove this deployment key from your repository settings. You won't be able to write to this repo with this key anyway.
Go to "Avatar -> Settings -> SSH Keys" and add the same key
Now try to push to remove branch
You were able to write to repositories before but this is a change in BitBucket where you're no longer able to write with deploy key.