Do retrofit ground wires need to be run in conduit?
Conduit or armor is only needed in certain cases

Retrofitted equipment grounding conductors (i.e. grounding conductors not run alongside the circuit conductors) only need the protection of conduit or cable armor if they are smaller than 6AWG and run exposed or otherwise subject to physical damage.   This is laid out in NEC 250.120(C):


  (C) Equipment Grounding Conductors Smaller Than 6 AWG.
  Where not routed with circuit conductors as permitted in
  250.130(C) and 250.134(B) Exception No. 2, equipment
  grounding conductors smaller than 6 AWG shall be protected
  from physical damage by an identified raceway or cable armor
  unless installed within hollow spaces of the framing members
  of buildings or structures and where not subject to physical
  damage.


Normally, unless you're dealing with particularly egregrious physical damage exposures, the armor on a Bare Armored Ground cable should suffice; upsizing the wire to 6AWG is also a suitable approach in many cases.