On Navy ships do the first officer's really spend much time on the bridge? I've heard that they basically run the ship for the captain and that they're all over the place so he doesn't have to be. Is that accurate? Because if it is it's unlikely Riker would have been on the bridge at the same time Picard was.
On the Enterprise, at least, neither the captain nor the first officer spends much time on the bridge. They are generally represented by the command duty officer, one of which is assigned for each watch section.
On a carrier, the first officer is indeed very busy with administrative matters, and has little time to take a role in the operations - i.e. use - of the ship. The captain and navigator (who fills the operations deputy role that the first officer is too busy to perform) both do appear on the bridge sometimes, the latter much more than the former. While I was assigned to the bridge, the first officer never made an appearance there.