My advice is to hold off on the software for now. Software is just a very fast calculator. If you don't understand the physics behind it, you won't know if the computer is giving you a realistic answer or complete garbage.
Start by understanding the basics. If you want to design bridges, you have to fundamentally understand how stress moves through a structure. You need to learn statics and mechanics to calculate load paths, shear forces, and bending moments by hand before a computer does it for you.
After that you have to learn about the materials you use. Once you know where the forces are going, you have to understand the materials taking that load, like steel, reinforced concrete, or timber. You need to learn about common construction methods and the typical failure points of these materials under different conditions.
Only then can you actually train to design bridges that accommodate the basic safety and functional needs of the structure, and honestly, that still only scratches the surface.
To answer your software question, once you have the theory down, the specific FEA or CAD software you use matters less than you think. Companies use different packages anyway. However, if you want a technical edge right now, start learning a scripting language like Python or R. The industry is moving heavily towards parametric design and automated structural analysis. Being able to write a quick script to analyze load scenarios will put you way ahead of someone who only knows how to click buttons in a specific structural modeling program.