Take a look at this thread:
The importance of being Solid
I've found that if trying to shoot without solid rear support my POI can vary significantly. I use front and rear bags from a bench, and rear bags when using a bipod in the field. Doing so minimizes the difference between them, at least in my experience so far.
Last fall we were trying various scenarios to prepare for a hunt. Going from bench to bipod didn't make much difference as we kept the rifles supported both times. Move to a standing tripod at 300 yards where you have no rest under the rear of the rifle and you're now standing as well... wow did those groups open up. A bit of an extreme example, but you'll see the same thing when prone or on a bench if the rear isn't supported too.