First, you need to prime the affected areas, the entire bathroom is a good idea. Use Kilz Oil Base as the primer. This will seal the green board's paper face and keep it from bubbling. Plus, the primer will make the imperfections easier to see.
Now you can do the repair(s). I like to use a setting type of <a href="https://www.house-painting-info.com/joint-compound.html">drywall compound</a> for most repairs. It is a powder that dries quickly. You can also use regular drywall mud, it is easier to work with. Spackling paste is more difficult to use, save it for small repairs. Apply 2 thin coats then sand. Use a medium/fine sanding sponge, it works a little better than sand paper.
After the repairs are finished and dry, prime the raw drywall mud then paint as usual.