I was thinking of running a 60 amp sub panel to a barn about 75 feet from the main panel. I've read that in a sub panel ground and neutral must be separated. However, can I just run three wires (hot, hot, neutral) to the barn, and drive a grounding rod at the sub panel, and leave the ground and neutral bonded in the subpanel? Thanks

No, the new feeder must be 4 wire, with two hots, one insulated neutral and one insulated equipment ground conductor.

The three wire method is no longer allowed.

Is there a particular reason this is no longer allowed?

4 wire system is safer than 3 wire.