How can I delete a repository in the new Bitbucket

Log into your Bitbucket account. Navigate to the repository you want to delete. Click the repository's settings icon. Choose Delete Repository from the left-hand navigation. The system displays the deletion dialog.

Version 2016:

Select your repo
Click the settings (last one in the left menus)
Scroll down the 'repository details' page
Click the 'delete repository' button on the right.

Version 2021 - navigate to the repository. In the left menu Repository settings and in the top right corner, there is the Manage repository dropdown menu with the option to delete the repository.