I have a 240 volt, 3-wire, 10 gauge feed from my house to a subpanel in a remote shed that has been there for at least 20 years. This feed is protected by a 30amp breaker on the house panel. There are no other metallic connections between the shed and the house The subpanel in the remote shed has one bus bar with the neutral connected to it. The neutrals and grounds of the circuits also connect into that bus bar. All of this is OK from what I can figure out (although not up to 2008 NEC). Here is where I am uncertain - the bonding strap from the bus bar to the panel case is not connected, and there is no grounding rod. Should the bus bar be bonded to the case and should I have a grounding rod with the wire connected to the single bus bar?

Well you are correct that the installation does not meet current standards. 2008 Nec requires that Neutral and Ground can only be tied together at the main service panel or disconnect.

I believe that you current installation would be grandfathered and does not need to be changed. However, if you upgrade the sub-panel system, then the entire system would need to brought up to code.

Currently you need a four wire feed to the sub-panel. Ground and neutral would need to be isolated from each other at the sub-panel and you would need to put in a ground rod.

The ground rod is not for the electrical grounding of the system, the ground from the 4 wire feed back to the main panel would take care of that. It is there to protect against lightning.

You need to install a grounding rod at the shed. Pick up a separate grounding buss and have your grounds (if any) terminate there. The grounding rod will offer lightning protection, as donf said.

If you plan on selling in the future, the home inspector(if thorough) might put it on the hit list to have another buss added to separate the ground wires from the neutral wires in the subpanel... So, if you feel like spending the money, it might save you time later to fix it now despite any grandfathering you're under at the moment.

Since this installation was done before 2008, it can remain a 3 wire feeder. Any installation done before a Code edition does not need to be upgraded to meet any new Code.

Yes, connect the bonding jumper from the neutral bar to the panel's metal box, be sure that all neutral and equipment grounds are connected at the neutral bar.

Install a # 6 copper wire from the neutral bar to at least one 8 foot ground rod. Some states, that are sandy or rocky soil, such as Maine, require at least two ground rods for grounding.

If a home inspector in the future tells you to upgrade to a 4 wire system, tell him to go pound sand. You are perfectly within your legal rights to leave it as is.

The National Electric Code is NOT retroactive, and applies to NEW installations.