I've been to 2 scenarios while bagging patients and moving.
1- The patient has been intubated and that means a paramedic is with you and your crew. If you are riding an minimum of 2 people, that means 2 people push/guide the stretcher and the remaining one bags. I've bagged while the medic and my partner have pushed the stretcher, as well as had a medic bag and I helped with the stretcher, no biggie.
2- The patient was not intubated and I was bagging (just my lone partner and I) He pulled the stretcher from the foot of the stretcher, and because the seal needed to be maintained, I "rode the rails." In other words, you put both feet on the bottom rail of the stretcher, lean all your weight forward so you are leaning over the patient, leaving both hands free to bag. Your feet shouldn't be touching the ground, "riding the rails" can also be used for CPR while moving into the hospital/ambulance. This worked because we weren't flying down the corridor and our patient was really thin, my weight added onto the stretcher and added stability and prevented us from flying out at the corners.
Hope this helps... ^_^