He could have had someone who knows what they're doing pull glass bits out of him. Jason could stumble around until he finds Damian. Or bother Drake, or try and pull them out himself from this angle, but Bigby seems intent on at least making sure they're out of him before he lets Jason fuck off, and Jason's - well. He's not finding a doctor, he's not going to go looking for Damian, who will just call him out for being an idiot for getting into unnecessary brawls.

So here they are: with Jason being much too tense, and Bigby quickly pulling pieces out of him. The lack of glass in him immediately causes the bleeding to get worse, given there's nothing in there to stem the flow. His jaw clenches tight with every piece that's removed, but he doesn't react outside of that. He's experienced worse, this is nothing.

"How're you gonna learn if you don't practice? If you're gonna be stuck in the middle of nowhere, you may as well learn to handle flesh wounds. I doubt this's the first you've come across, and it won't be the last." Why not use Jason as a dummy, he's durable. Even if he's beginning to get a little lightheaded, it's nothing he hasn't powered through before.