Bridge
The Bridge (more accurately the Wheelhouse) is the area from which the RMS Titanic was commanded, housing the ship's steering gear, engine-order telegraphs and other paraphernalia.
It is located on the forward-most part of the Boat Deck. The officers' quarters were located directly aft of the Bridge, though they are inaccessible by the player.
Accessibility
Passengers are not usually allowed on the Bridge. However, if Frank Carlson finds Third Officer Morrow's lost binoculars and gives them back, he will be allowed on the Bridge so long but Morrow doesn't want him to touch anything. This is true for the seaman guarding the starboard entrance, as well.
When Professor von Haderlitz is killed and Third Officer Morrow has gone to the entrance of the Turkish Bath with Steward Smethells, Carlson will be able to sneak onto the bridge via port side, as Morrow is no longer present there, whether or not you have found the binoculars.
An hour after the Titanic has hit the iceberg and is sinking, the seamen do not let any passengers on the Bridge.
Trivia
Along the aft wall of the Wheelhouse are four telephones connected to the boiler rooms. These, along with the ship's wheel, are the only things that can be interacted with on the Bridge. The player may not interact with the engine-order telegraphs or any of the doors.
Attempting to alter the course of the ship using the wheel, even by a single degree, will earn a harsh rebuke from Third Officer Morrow who will immediately correct the ship's course and heading. Oddly enough, Morrow will not do this until the player 'leaves' the wheel, meaning one could alter the course for several minutes before it is corrected. Despite this, there is no way to prevent the ship from hitting the iceberg. Even if you walk into the wheelhouse when Morrow is guarding the door of the Turkish Bath after the murder, he will still pop up after you turn the wheel and leave.
Though there were numerous other crewmen and officers on duty the night of the sinking, only Third Officer Morrow and the unnamed crewman are present.