Unless something has changed, plain AutoCAD does not have a command to export a shapefile. In order to export from AutoCAD, you probably want the mapexport command. That comes with AutoCAD Map 3D and probably with AutoCAD Civil 3D. If you can get Map without Civil 3D (assuming you don't need Civil), that's the way to go.
If the surveys you wish to export use arcs, you may want to use ArcGIS Desktop to export the CAD data into a geodatabase. Sounds like you have done this already. I say 'export' but this is confusing because ArcGIS Desktop reads CAD files directly. Arcs are not supported in shapefiles. The arcs are mimicked with short little line segments (tessellated curves?).
Paul Lohr