The captain would take the helm going into and out of port. His helmsman would be steering at most other times, and seeing as ships pass port-side to port-side, it would make sense that the helmsman is on the left.
This may happen on smaller craft but a ships captain and the pilot will be present on the bridge when leaving port. The helmsman will be acting under the pilots commands until the pilot disembarks, then generally the bridge watchkeeper and helmsman may continue until clear of traffic when the autopilot may be selected. In deep sea transit the autopilot usually manages the helm unless heavy traffic or heavy weather dictates the use of a helmsman. From my experiences (23 years at sea) the captains chair on the bridge is normally situated more towards the port side of centre.