Gronding requirements for standby generator
That is correct

You are correct that the bonding means in the generator should be pulled in this case since your transfer switch has a solid neutral; in this case, since you have a service entrance transfer switch, your bonding means will be in the transfer switch, with the "main panel" wired as a subpanel from the transfer switch.

You are also correct that a grounding electrode conductor does not need to be run to the generator location; the equipment grounding conductor from the transfer switch to the generator is sufficient to bond the generator to the grounding electrode system.  (There's no requirement for local ground rods at the generator, by the way: NEC 250.32(A) says "building(s) or structure(s) supplied by feeder(s) or branch circuit(s)" need a grounding electrode system of their own, but your generator's not supplied by anything.)