How to ground a 240v outlet in a service panel with ground bar?

This is a basic installation... can you be more specific with your question?

The service panel has there hot lines,
One neutral bus and no grounding bar. Where does the grounding wire from the new 240v outlet go? Can it be connected to the neutral bus?

Is this the main panel in the building? If so, then both Neutral and Equipment Ground conductors terminate on the Neutral bar.
Verify that the Neutral bar is "bonded" to the panel enclosure.

Where is this? Is it a commercial building?

Commercial building in the Bronx,NY.

Does the panel in question contain the "Service Disconnect" for the building?
Or is this panel the second of third in the building...

Commercial building in the Bronx,NY.All electrical work in NYC requires a licensed electrician.

There are dozens of ways to do this wrong... your silence is one of them