Bridges are secret teleporters that take you to a level in the next stage. Normally teleporters only go to other levels within the same stage, so you cannot skip the boss at the end of the stage.
The only bridges are in Isle of the Lion Lord and in Hoverboard Beach. It is impossible to use both bridges in a single playthrough.
While the first bridge leads from Isle of the Lion Lord to Elsewhere 8, and thus from Stage 1 to Stage 2, the bridge from Hoverboard Beach ends in Frosty Doom, thus leading from Stage 2 to Stage 3. One might think that there should be a bridge from Stage 3 to Stage 4 as well. This is unlikely, however, since in the 31 years since the game's release nobody has been able to find it.
Note that the second bridge comes at a steep price, as it inevitably takes you to the horrific Bloody Swamp. You'll very likely blow more lives here than taking the long way. Go ahead, if you think you have the skill...