What is the correct verb for 'driving' a ferry?

Captain is a verb; and pilot is a possibility too, although that has a specific meaning with regard to ships [a shipping pilot is usually someone who is locally skilled and will successfully negotiate hazards around a harbour].

captain
verb [with object]
be the captain of (a ship, aircraft, or sports team):
   all the boats are captained by professional sailors
noun
the person in command of a ship

pilot verb (pilots, piloting, piloted)
[with object]
be the pilot of (an aircraft or ship):
   he piloted the helicopter from Paris to Deauville
noun
a person who operates the flying controls of an aircraft

[ODO]

A captain (as well as captaining) navigates (guides it over its route):

navigate verb
2 [with object] sail or travel over (a stretch of water or terrain), especially carefully or with difficulty:
   ships had been lost while navigating the narrows
   the drivers skilfully navigated a muddy course
  • [no object] (of a ship or boat) sail; proceed:
      [with adverbial of direction]:
      we sailed out while navigating around large icebergs
  • guide (a vessel or vehicle) over a specified route or terrain:
      she navigated the car safely through the traffic

[ODO]

In addition to the other answer's "captain", I would add "helm" to refer specifically to the person and act of operating the steering controls - a captain may be moving around the bridge for a better view, giving instructions to the helm.

While I agree with the other answers, there is nothing wrong with steering a ferry. At least, it sounds right to me and the Free Dictionary seems to agree with me (emphasis mine):

steer
v. steered, steer·ing, steers v.tr.

1. To guide by means of a device such as a rudder, paddle, or wheel.
2. a. To direct the course of. See Synonyms at conduct.
   b. To maneuver (a person) into a place or course of action. See Synonyms at guide. v.intr.
3. To guide a vessel or vehicle.
4. To follow or move in a set course.
5. To admit of being steered or guided: a craft that steers easily.

The word's etymology also supports nautical usage (emphasis mine):

steer (v.)
"guide the course of a vehicle," Old English steran (Mercian), stieran (West Saxon), from Proto-Germanic *steurijanan (cf. Old Norse styra, Old Frisian stiora, Dutch sturen, Old High German stiuren, German steuern "to steer," Gothic stiurjan "to establish, assert"), related to *steuro "a rudder, a steering" (cf. Old English steor "helm, rudder," German Steuer and first element in starboard), from PIE *steu-ro- (cf. Greek stauros "stake, pole"), from root *sta- "to stand" (see stet).

The notion is of a stiff, upright pillar or post used in steering.