Falcon 9 is 3.7 metres in diameter, whereas Starship and the super heavy booster will be 9 metres in diameter.
First, I'd like to point out that since Starship and Super Heavy can only be transported vertically, your estimation of the height difference between a Falcon 9 transport and a Super Heavy transport is off by a couple orders of magnitude. The height of a transport that is trying to pass under a bridge wouldn't be 3.7m vs. 9m, it's 3.7m vs 70m.
How do they intend to transport these spacecraft?
There are two aspects to this answer:
- They're rockets. They can fly, there is no need for them to drive on the road.
- SpaceX wants to build hundreds of Starships. There is no reason to believe those would all be built in a single factory. SpaceX could just build them near to the launch pads.
And of course, you can combine those two: build near a major space port, then fly to your actual launch location from there.
SpaceX has already demonstrated that it is possible to build Starships within weeks or at the most a few months pretty much anywhere, even in an empty dirt field with no infrastructure. They have also demonstrated that it is possible to build mass-Starship factories within months or at the most a few years pretty much anywhere, even in an empty dirt field with no infrastructure.