first, I would focus on either roads or bridges - but not both.
I'm not sure you will ever be able to both design and build them as a contractor. Do you prefer engineering/design or construction? If construction, you don't necessarily need an engineering degree to own or manage a construction company. If design, then get a degree in structural engineering, go for the masters in business adminstration and then start up a bridge design firm. In the meantime, see if you can get a job with your state department of transportation where you can get experience with all of it.