24th Century Federation Bridges

[Jedman67]

Magic?
Presumably, all bridge modules have standard connectors to "plug" into the rest of the ships power, water, life support, sensor and elevator systems. It's entirely possible that each module has a small turboshaft that aligns (out of sight) to a standard turbolift junction.
The more likely explanation is that bridges are designed to be able to be installed with only a few weeks/months head time in Spacedock (rather than need to be built up from scratch), and engineers don't have to be extremely creative in aligning stuff up, rather than "plug n play" like a USB thumb drive.

 

[FormerLurker]

As seen from ST IV-VI, the bridge modules probably are built with different design specs inside the bridge itself, but all the outsides are common to a predesignated plan. What's between the outer shell and the plugs on the bottom is where all the differences are. And since the E-A had at least three different bridge designs over its working life, some designs may work, and some may not. All that fixing Scotty did on the bridge for three weeks may well have been attaching the new module in an effort to get it to interface with the rest of the ship properly, because the first bridge module didn't work.