Atlassian accounts (id.atlassian.com) and Bitbucket Cloud accounts (bitbucket.org) have separate user systems and they also have separate 2FA systems:
- Atlassian 2FA: https://confluence.atlassian.com/cloud/secure-your-account-with-two-step-verification-939505063.htm
- Bitbucket Cloud 2FA: Secure your account with two-step verification
If both are enabled, the user would be forced to authenticate through 2 different 2FA screens separately.
Note: On the Bitbucket Cloud side, if the user has enabled "Require 2FA to access content" as per Control access to your private content, this will only enforce Bitbucket Cloud 2FA and not Atlassian 2FA.
Therefore in situations where the organization needs to enforce 2FA on Atlassian accounts and Bitbucket repositories, the users will have no choice but to go through 2 separate 2FA screens.
Allow users to login into bitbucket.org without authenticating through the Bitbucket Cloud 2FA if they have already authenticated through Atlassian 2FA.