Was this ever resolved? I am now having the same issue on projects that have been set up within the last month. We are just at the stage of moving tickets over to the new projects and of a sudden our users (one even set to site-admin) not can't bulk edit the Sprint Field.
You might have permission to transition some of the issues, but the bulk-edit needs you to be able to transition all of them.
Your admin and global permissions are not project permissions, you'll need to identify which projects you do not have permissions to.
Try taking your query for the bulk edit and running it with a "and project in (xxx, yyy, zzz)" clause added. For each project the main query includes, add the project to the clause and then check you can transition one of the issues returned.
You're right, if you can transition an issue from the issue view, then run a search for it and try bulk-edit on just that one issue, and it does not offer the transition rights, then there's something broken.
The problem for me is that I've only once been able to get Jira to do that. I can either transition that one issue via view, board and bulk-edit, or I can't at all (assuming the same user is in use - I've had some really interesting ones where users look identical, but three's some obscure setting that blocks one and not the other)
The exception was when I had a condition on a transition that I should have been able to pass. The code for it was broken - it worked on issue view, but crashed on bulk-edit (which effectively returns "no, this user can't transition this").
That is a pretty obscure error though, and it was my fault (my code in the condition). It does make me think we should take a look at the logs - ideally, have a terminal and a browser open, run your search as normal, then start tailing the log as you select "bulk edit" and go through the process.