The github repo is private, so I set the authentication on and use a Github access token.
The token is proven good, because I can do a local clone using the same credentials. The same credentials work in SourceTree.
The repos is roughly 250M once on disk, and has two git submodules. No LFS support.
I have just tested this on my end and was able to import my own Github repo to my personal workspace using a personal access token.
Are you able to generate a new personal access token with everything ticked under the repo scope as a minimum? Ensure once the token is generated that this is copied and pasted to the clipboard, once you're in the repository import tool - ensure that authentication is ticked, the correct username is entered (a username who has access to the repo in Github) and that the PAT is copypasted into the password field.
If this is a private repo, you need to make sure it is imported into a private project.
You will also need to have write access in Bitbucket Cloud to be able to import the repo.
Try this and let me know how it goes.
- Ben (Bitbucket Cloud Support)