Summary

Visual Studio asks for credentials (Atlassian login) each time a push is made. 

Diagnosis

Atlassian login credentials are not required for making a push to Bitbucket. Atlassian deprecated login passwords for app passwords. This happens due to an old version of a Bitbucket plugin on Visual Studio. 

Solution

You can resolve this with a couple of entries in the git config entry - 

git config --global --replace-all credential.interactive false
git config --global --replace-all credential.modalPrompt false

These two entries will disable the Atlassian login prompt. You can also edit the global git config directly with this command and enter the text - 

git config --global --edit

Enter the following in the text file - 

[credential]
    helper = manager
    interactive = false
    modalPrompt = false