According to this article I can install bitbucket via unattended mode
Is there the way to get full tree of possible parameters?
For example I need to answer on next questions:
Would you like to install or upgrade an instance?
Install a new instance [1, Enter], Upgrade an existing instance 
Install Bitbucket 6.9.1
What type of instance are you looking to install?
Install a Server instance [1, Enter], Install a Data Center instance , Install a Smart Mirroring instance 
The easiest way to get this information at the moment is to run through the installer as normal and choose the options when prompted that you want to use. After the installation completes, this will create a response.varfile inside <APP_INSTALL_DIR>/.install4j
You can make any changes as needed and supply it to the installer with the -varfile option.
When I ran through this with the default settings, this was the response.varfile created for me and should give you an idea of the options available:
# install4j response file for Bitbucket 6.9.1
This installs Bitbucket Server as a service, starts it, and does a new installation.
installation.type has the following valid options: UPGRADE|INSTALL|MIRROR_INSTALL|MIRROR_UPGRADE|DATA_CENTER_INSTALL|DATA_CENTER_UPGRADE
Beginning on April 4th, we will be implementing push limits. This means that your push cannot be completed if it is over 3.5 GB. If you do attempt to complete a push that is over 3.5 GB, it will fail...