You need to start the builder a bit earlier, so that the end of the bridge, or at least close to the end of it, is under the end of the platform.
Note that you are NOT wrong about that the builder needs to be turned by a blocker. The last few bricks just need to also be under the end of the platform.
The most important trick of all is that the bomber, as well as making the fall safe, also creates a small hole in this bridge so the lemmings can get down.