I have a question about my sub panel that I'm installing in a shed in the back yard. I'm using a 3 wire feed from the main panel to the sub panel (H-H-N). ...because I'm using the 3 wire feed, I'm going to be putting in two ground rods no less than six feet apart with a continuous 6 gauge wire connecting the rods to the ground bar in the sub panel. I know that you're not normally supposed to bond the neutral bar in a sub panel, but is that because you normally have a ground wire in your feeder? Should I bond the neutral bar in this case because I don't have a ground wire feeder? Or should I still keep it un-bonded?
If you're in an area that has adopted National Electrical Code, you'll have to run a 4 wire feeder. You'll also still need the ground rods at the shed, which you'll bond the grounding bar in the panel to.
If it's an existing 3 wire feeder, and there are no other conductive paths between the buildings. Then yes, you'd bond the grounded (neutral) bar. However, if there are other conductive paths between the buildings (water pipe, conduit, gas pipe, etc.), then you'll need a 4 wire feeder.
If this is a new installation, you'll need a 4 wire feeder.
Ground rods are not a substitute for a ground wire. They do completely different things. Ground rods cannot do a ground wire's job because dirt is a terrible conductor. It cannot return enough fault current to trip the breaker, for instance.
Ground rods are to return natural currents like ESD and lightning.
Bonding neutral to ground in a subpanel would be even worse than hooking it up to only the ground rod, which is still bad.
If you are stuck with the 3-wire feed, go 120V-only... or 240V-only... or 240V for most loads and a 120V transformer for a few 120V loads... or a large transformer and make this a separately derived service.