Exactly as the title says: how do I get a captain to become a bodyguard for a warchief? There doesn't seem to be an option; all you get is kill or betrayal options, as far as I can see.
In order to get an Uruk of your choosing to become a bodyguard you'll need to advance far enough into the story to issue commands to branded Uruks.
You will know how to do it by the time you finish that story mission, you also won't be able to do it before then.
Here's a reminder in case you forgot how it's done:
- You need to brand a captain (the future bodyguard) using either Stealth Drain (if he's vulnerable to stealth), Combat Drain, or by choosing the "Dominate" option when you get the chance to finish him off.
- Grab the branded future bodyguard and "Dominate" him (this is the same move as when you interrogate Uruks), then select the "Command" option.
- Choose the warchief your captain is supposed to guard.
- Start the captain's "Power Struggle" mission and help him if necessary.
Once the Power Struggle is complete, your captain will be promoted to bodyguard and be assigned to whichever warchief you chose earlier.
Uruk captains can also get promoted to bodyguard without your help, but you won't have control over who guards whom. Simply make sure every captain is branded, so the warchiefs can only choose branded Uruks to guard them.