The airport already probably outperforms, especially given its physical and surface connectivity disadvantages, so it is reasonable to speculate how much busier it would be at a bigger and better connected site.
Currently £600,000 is being spent on a study into improving surface connectivity. The airport and the local authorities in the area recognise the poor connectivity, albeit the A1 Flyer bus from city to airport now uses a dedicated busway and a section of the new South Bristol Link Road for part of its journey, which at least gets it away from the worst of south Bristol traffic bottlenecks. Bristol's elected city mayor wants an underground system for the city and his anchor route would be to the airport, although that would probably be mainly above ground outside the city.
Before any of that could happen though the airport has the task of obtaining planning permission for its current 10 mppa limit to be raised, a not inconsiderable one in the face of current hostility generally and in the area locally to airport expansion.