I guess I'm stupid. I'm supposed to find someone who's always resting for the doctor. I've looked all over the map and I can't find any of them anywhere.
Viewing post in Broken Dreams Correctional Center comments
To force an encounter with any known NPC - in this case, one of the targets listed on the bounty board - you can force an encounter with them via:
Me -> Encounters -> Characters.
Sometimes you might need to move to a different spot for this to work (and it'll say so). For example, if you're in Medical, you might have to move into the Cellblock area to force the encounter with an inmate.