If you are looking to prevent users from changing the source code during a specific time frame, we don't have such a feature available out of the box.
You can temporarily change the permissions of users and user groups to a certain repository to Read (this way they won't be able to change the source code of the repo), and then switch back to the original permissions.
You can do it from the Bitbucket website, if you open a repo then go to Repository settings > User and group access
Alternatively, you could also use our APIs to write a script and change the permissions to Read (and then change them back to the original permissions):
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...