Can I terminate a ground wire to the neutral bus if the ground bus is full?
Mixing Grounded and Grounding
If this panel serves as the main disconnect, and the grounding and neutral bus bars are bonded. Then yes, you can terminate both grounded (neutral) and grounding conductors at the same bus bar.

Notice that the bus bars are bonded using a bonding strap.
Multiple Conductor Terminals
If the bus bar is able to accept multiple conductors under some or all of the terminal screws, it should be labeled as such either on the bar itself or in the panel documentation.  Terminating multiple conductors under a screw that is not rated for it, can cause bad connections, excess heating, damage to the conductors, etc.
Additional Bus Bars
Some panels are configured to allow additional bus bars to be installed. If your panel is one of them, you could install an additional bus bar and terminate extra conductors there.  Other panels may accommodate extended (longer/larger) bus bars, that can be installed in place of the existing bus bars.