It's a tough one.
You already have good advice here.
I also think talking to the bully doesn't really achieve anything. The coach should already know and if not that worries me, and it's really not your job.
I'd give friendly advice to the noob, "Saw you had a tough round there! Honestly that's me most weeks. When you're already tired and you get someone who goes a bit rough, you can try and last through it a while, but don't be afraid to tap out while youre still learning. All good training partners will understand, we've all been there." Get's a small dig in at the bully if you want them to hear too
You could just wait to another session, "Saw you had a tough round last week, don't worry about it! etcetc, try XYZ next time!"