You can connect your GitHub and Bitbucket accounts on CircleCI by first logging in with your primary account (e.g. GitHub), then clicking your avatar (top right) and selecting 'User Settings':
On the next screen, you can connect your accounts:
After this is done, you can use the 'organization picker' (top left) to switch between accounts:
The icon on the right shows whether an account is associated with GitHub or Bitbucket.