There are two acceptable ways to deal with the neutral and bonding. The key concept here is that the nuetral must be bonded to ground once, and exactly once, regardless of what else you do. Speaking as an engineer, pick one of these two:

1) Float the neutral at the generator, and bond it at the main panel or ATS. No additional ground rod required.

2) Switch the neutral at the ATS, and bond it to ground separately at the generator and service disconnect. You can run the ground wires right back to the same main bond if you size and bond the conductor properly.

Also note that for the generator, the ground is functioning only as a safety ground and not a parallel conductor for neutral current returning to the substation.