BVMs are just there to force gas in. I don't like the phrase "breathing for the patient", that's what ventilators do.
With the BVM you only perform part of the breathing cycle, the rebound of the patient's intercostal muscles and diaphragm do the rest of the work in exhalation.
That's why we generally equate adequate BVM breaths with chest rise and fall.
Also remember that non-rebreathers deliver about 60-85% oxygen and BVM's can deliver 100%. Because BVM's are more for CO2 removal, they can work perfectly fine without an oxygen source.
To clarify the above statement, BVM's do breathe for the patient as they are also known as manual resuscitators or manual ventilators. Mechanical ventilators (while fancy on breath delivery) also require the natural elastic recoil of the chest and lungs for exhalation. Ventilators don't "suck" the air back out of the lungs. All you can control is the inhalation aspect of the respiratory cycle. Non-rebreathers are only oxygen delivery devices.