Problem Definition
Currently Bamboo requires the use of a Personal Access Token (PAT) which is not recommended by GitHub. With a PAT customers are subject to lower rate limits and the need to use a shared service account.
Also, once token is generated they need to individually add it to every linked repo that needs that access. If at any point it's entered incorrectly it will possibly lock the account.

Suggested Solution

Establish an OAuth2 connection between GitHub and Bamboo, that would transfer secret and client ID (OAuth2 is a protocol that lets external applications request authorization to private details in a user's GitHub account without accessing their password.
Currently, we do have that option for Jira Cloud -https://support.atlassian.com/jira-cloud-administration/docs/integrate-with-github/
We also have an app in Jira for GitHub - https://marketplace.atlassian.com/apps/1219592/github-for-jira?tab=overview&hosting=cloud

Give an option to customers to clone a GITHUB repository in Bamboo without using a PAT token