Star Trek uses naval terminology, specifically those terms used by the U.S. Navy and probably those closer to the Navy in the 1940s, 50s, and 60s... one notable reason for this is Trek lacks dedicated carrier classes in favor of ships that seem to be dedicated battleships (Battleship doctrine is largely obsolete in a Modern Navy, as Carrier doctrine is superior).
So in naval parlance, a Bridge is a specific area of the ship where the command staff could issue orders (such as turning the ship or speeding up or slowing down). Historically, these were called to the actual offices that controlled the ship (Helm/Conn or Engineering department) since remote operations of these areas was not possible. Thus, the structure was created to go over the ship for viewing on all sides by decision makers and usually included a dry pilots house for navigation and communication offices could be heard in rough weather. Because this structure went "over" a ship so nothing was blocked from the captains view, it was called a Bridge... modern ships do not need this type of structure, but the control area of the ship is generally still called a bridge.
A deck, by comparison roughly corresponds to a floor or level on a building, though in reverse order (Deck 1 is the upper most deck where as the higher the number, the closer to the bottom of the ship you go. Pleasure vessels such as cruise ships will often use Letters instead of numbers, but A is the top most deck.
When when all else fails, google US Naval terminology and use them as as they do.
Also fun fact: The official Klingon Language does have a term for a nautical bridge, but no term for a a bridge in the sense of "A bridge over troubled waters". Given that Shakespeare has two plays set in Venice, one must assume the concept of that type of Bridge is not alien to Klingons... just that no canon term was ever created.
Edit: To answer @Dan's question:
While you are correct in that the Enterprise was named after a Carrier, up until Pearl Harbor, the Navies of the world operated under Battleship Theory, which basically made Battleship classes the focus of naval engagements. Pearl Harbor and Midway proved the viability of Carriers as a superior weapons platform as they were able to do more damage from a further range than Battleships, though the Flags of the day were still the BBs. Prior to WWII, Carriers weren't fielded in war in a serious manner, and the Treaty of Washington, which sought to limit the naval arms races which contributed to the first World War, Carriers were still seen as experimental vessels and thus not limited under the treaty. Though the treaty was largely inefficient as everyone cheated. In fact, even today, Treaty of Washington style cheating is still well entrenched in Navies of the world. For example, The U.S. officially fields 11 Carriers... which are the Nimitz Class and Ford Class Super-Carriers (only nation to field Super-Carrier Classes). In addition, the U.S. has 20 "Amphibious Assault" class vessels... which are ships that can launch aircraft but are definitely not Carriers (Despite being larger than the majority of non-U.S. carriers in the world). Due to various international laws, Russia and Japan do not field carriers either. Russia has an Aviation Cruiser, to avoid a restriction on movement of capital ships into and out of the Black Sea (Russia's only western warm weather port... the straits for access are controlled by NATO ally Turkey and by Treaty, Capital Ships are not allowed through the straits, which carriers qualify as, but cruisers do not). Japan has a Helicopter Destroyer, which is so named because Japan does not have an offensive military force, and Carriers sound too offensive... especially when your nation proved the superiority of Carrier Theory over Battleship Theory... by using it against what is in present day their closest military allies.
While Carrier Theory was strongly practiced by the US during the Pacific War, it was more out of necessity than superiority, as the Carriers were the only part of the Pacific Fleet that survived the bombing of the Pearl Harbor. It was still seen into the sixties that Battleships were the pride of the Fleet. The last of the U.S. Battleships, the Iowa class, were retired from service in the early 1990s and even then were still romanticized and the push back against the retirement was strong enough that all four of the original Iowa Class are Museum ships.
It should also be noted that while the Enterprise that the Star Trek ships were named after was the Enterprise-Class Carrier (Class unto itself), the name U.S.S. Enterprise has been used by several ships in the United States Navy dating back to the original 8 commissioned ships. The current U.S.S. Enterprise is the third carrier in the Gerald Ford Class of Air Craft Carriers. It should also be noted that the original plans for Star Trek were going to call the space ship the Yorktown, until announced plans for the Enterprise-Class included that it would be the first Nuclear Powered Carrier, which seemed as cutting edge to the 1960s as a space ship. For his own part, Gene Rodenberry was an Army man, not a naval one, and probably did not have much conceptual knowledge in the difference in carrier theory to accurately portray it. That, along with budget constraints making smaller craft tied with the ship difficult, the focus on a more Battleship styled space navy seemed better suited (additionally, Carriers in Space do not work well without some hard rules to say why they work).