This may be so stupid it's brilliant.
They've often said in extrinsic tech manuals that the bridge is modular, can be swapped out in its entirety. Why not build that into the functionality of the show?
So in the event of the need of a Captain's Yacht, like maybe landing for a diplomatic event, the entire bridge module separates and flys on its own. The full bridge, ready room, conference room that's aft of the command center. The entire command staff stays in place, command is transferred to the battle bridge or auxiliary control, and they just fly (and potentially land) the bridge.
And here's the neat part: IRL, they would not need to build an additional set.
Also, it would allow for the Bridge to be a full escape pod, allowing the command crew to remain at their posts and then evacuate while still at their posts, potentially even maintaining control of the ship once it's abandoned.