How to know my permissions for bitbucket repo?
As per new bitbucket you see the permission details, once you click the 'clone' side menu.
Refer the screenshot
Note: As bitbucket tend to change UI multiple time(s), this answer may subject to not work for you. As of April'2020 UI was as given in screen shot.
As of today, Access Level is visible on the vertical panel on the right side of the Source/Master page of the repo. See this screenshot.