Linking GitHub and BitBucket accounts for public builds

I wanted to try automated builds, but it seems that I need to give Docker Hub full read/write to all my private repositories, even though I only want to build from public repositories. It allows more restrictive way of linking my GitHub account, but then I can’t access repositories in my public organizations, so it’s not going to work.

Is there any way to use automated builds without giving Docker Hub accesses to unrelated private repositories?

I thought I could work it around by creating a separate BitBucket account, to which I gave admin rights to the (public) repositories that I want to build, but I can’t see the repositories when creating an automated build on Docker Hub. So it looks like it needs full admin rights for the organization.