Hello, I have a GE subpanel with four circuts on it, one still empty. I wanted to add another circut/circut breaker and when I opened the subpanel I expected to see two bus bars, one for the white/neutral wires and one for the bare ground wires. This panel has only one bus bar with eight holddown screws. This bus bar has mainly bare copper wires connected to it but it also has a couple of white wires on it. This subpanel is not bonded, the main service entry is the one bonded. Does this seem correct? I was at a loss as to where to connect the new white and new bare copper wire to even though the bus bar still has empty slots.
Any sugestions would be greatly appreciated before I hurt myself!

A sub-panel is required to be fed by a four wire feed. I believe that your panel will be fine since it appears as though your sub panel is only using a 120 VAC supply. That is why there is only one phase bus bar.

However, Neutral and Ground cannot connected or bonded together anywhere but the Main Service Panel.

If both White (Neutral) and Bare Ground are connected to the same block, you have a code violation. You will need to add a neutral bus and make sure it is isolated from the ground bus bar.

Is this sub-panel in a detached structure?
An older installation in a detached structure could easily be as you describe and be perfectly legal.

If this is within the same building as the main then it is wrong.