I completed Blind Betrayal, went out on a mission with Danse post-MQ (best ending option), and dismissed him to return to his bunker. Went to find him later, and he is gone. I have searched all my settlements just in case I accidentally sent him somewhere else and cannot find him.

Is he dead on the road back to the bunker somewhere? I've done back a couple of times after quite a few game days have passed. Still no Danse.

I'm on Xbox, so I can't find him with a console command. Any ideas?

Better forget about him - at least as a companion - for now.
Having him with you when you're roaming about as the BoS Sentinel will turn any Brotherhood you encounter HOSTILE.
Even within the Diamond City marketplace...
Not good, right?

As the Sentinel, I used to go visit him in his bunker now and then.
But that's where he remained!

Hey, I weaseled his life out of Elder Maxson - and not so he could be slain by my Brothers while out roaming around the Commonwealth...
Which is probably what happened to your Danse.
Since the BoS controls all the checkpoints on all the roads everywhere.
And ol' Danse, he's kinda hard to miss, heheh... I mean, stealth just isn't his thing, y'know?

I remember in Oblivion that I came upon Mazoga the Orc dead in the road just outside the house we used. I'm afraid that I'll be roaming around in Fallout and find Danse in a similar condition.

Check the Boston airport ruins.

I loved Mazoga the Orc! She was great.
I was actually really proud of her when she was made Knight Errant (and she asked me "that's... good, right?)
Not sure but I think I made her 'essential' - for the very reason you described.
That's Lynda (Magnolia) Carter's voice too, BTW...