BIF:
I'm just going by what I've read on this and other Prius boards. What I've read is that zero bars is 25% of battery capacity, and that, with the possible exception of very extreme circumstances (?), the computer will not let the battery go below that. (For considerations of battery life: you are deprived of about half the battery's physical capacity, and in return your battery will last the life of the car.)
I do not have the link at hand, but I read a fascinating description of what happens when you accelerate from a stop. (Possibly from Graham's site.) Basically it's like this:
As you start out, the ICE is spinning but the wheels are not, so the torque the ICE applies to the wheels results in no power transfer. The ICE turns MG1 instead, which gives electricity to MG2, which turns the wheels. Depending on how hard you press the pedal, additional power may be drawn from the battery for MG2. As you begin to move, more power from the ICE goes directly to the wheels, and less goes through MG1 to MG2. Note that the ICE can be turning at a relatively constant rate the whole time, keeping it within an efficient range. The faster you go, the more power is transfered directly from the ICE to the wheels, and the less goes through MG1. Once you reach a constant speed and the power requirement to move the car is minimal, the power going to MG1 can be used to recharge the battery instead of going to MG2 to help drive the car; or the ICE can shut off entirely and the car can be powered by MG2 directly from the battery, until the SOC drops to where the car starts the ICE to re-charge the battery. The torque from the ICE is always split at a constant ratio between the wheels and MG1 (60:40 ?????) but the relative speeds of the different components determine the ratio of the power delivered on the two different paths.
It is true that there are losses due to inefficiency whenever you convert mechanical energy to electric, or back, so the path ICE-MG1-MG2 involves inherent losses. However these losses are dwarfed by the gain in efficiency from allowing the ICE to always run closer to its design rpm.
You are not improving things when you accelerate on electric, because then all your acceleration energy comes from the battery and encounters the conversion loss. If you accelerate normally, allowing the ICE to run, then some of your acceleration energy is direct mechanical transfer from the ICE to the wheels once the car has begun moving.
This explains John's recommendation (supported by others) to accelerate using the ICE, and only try for electric after you are up to speed. In other words, "Just drive it!". Exactly the same techniques for improving mileage work for the Prius as for other cars: moderation: don't abuse it, but don't baby it.