You can rebind your organisation by following these steps:
Go to your BitBucket Workspace → Settings → Installed apps and remove the SonarCloud app. This should effectively unbind your SonarCloud organization from BitBucket Workspace
Log in to SonarCloud with your BitBucket account and verify that your organization is unbound - the BB platform logo will be grey, you can also verify this in Administration → Organization settings
Log in to SonarCloud with your GitHub account (which has to be already a member of your SonarCloud organization), go to your Organization → Administration → Organization settings and you should have an option to Bind this organization to GitHub (see screenshot)