Change the password itself with your provider — Google or Microsoft — on their own website. BlueMail cannot change it for you, and for security reasons it cannot reset it either.
Once you have changed it there, point BlueMail at the new credentials:
- Open Settings | Accounts.
- Tap the account you want to update.
- Tap Update Password.
For Gmail and Outlook this does not ask you to type a new password into BlueMail. Both use OAuth, so you are sent to Google's or Microsoft's own sign-in page and BlueMail receives a fresh token when you finish. See Gmail, Outlook and how OAuth works.
Accounts that still use a plain password — most other providers — will prompt for it in the app instead. See updating your account password.