Give your player a reason to not even *try* to escape.  Create some sort of subplot revolving around another prisoner, something that you know the PC would have to stick around for.

Maybe someone is in desperate trouble, or has information the really PC needs.  They say that they can help the PC escape once their own mission is accomplished.  (Maybe they're lying, or maybe the plan will seem like it failed until the NPC comes to the rescue.) The player will presumably trust that you won't screw them over for following an obvious plot hook, so as long as it isn't against their character and there's nothing else tempting to do, they'll take the bait and not actively look for other avenues of escape.  

This gives them their own plot that's (mostly?) independent of what the NPC is doing.  You could cut between the two plots like a TV show to provide the proper pacing.  Ideally they'd somehow connect in an unexpected way at the end, but that might be hard to pull off.  :)

A lot of people have mentioned that focusing on NPCs too much is bad for a game, but I imagine its hard to avoid *all* elements of that if you only have one player.  Just try to pay attention to whether that player is getting bored or zoning out.  ;)