STAAD is a general purpose program for analysis and design of structures modeled using lines, triangles, quadrilaterals and blocks. It is not a customized software for bridge design.
You could model the beam-slab combination using members and plate elements. The vehicle loads can be applied using the moving load generator, or using the add-on program BEAVA. For the former, see example 12 in the Application examples section.
The concrete design commands have a provision for designing T beams and rectangular beams. For designing the slab, go to the built-in Concrete Design mode, or use an add-on program like RAM Concept.
If none of this appeals to you, look for the Bentley Bridge offerings like LEAP.