I don't think of it as bouncing my arm off my body. However, I do want my arm to solidly connected to my body when force is transferred from the bell to the hips on the downswing, and from the hips to the bell on the upswing.
I want to delay folding at the hips until the arm makes contact withe the body (I've seen Dan John use the cue "play chicken with the bell"). I never want to start hinging in anticipation of the bell before my arm is connected to my body. Then I want the bell to drive my hips back.
But I want the timing and force transfer to be as smooth as possible. "Bouncing" off the belly implies to me an overcorrection in the other direction, delaying the hinge TOO long until the arms HIT the body.
Also, I don't want to drive the hips forward too soon out of the hole. I want to let the bell (and my hips) complete its full backward movement before driving my hips forward. If you try to drive the hips forward too soon, while the bell is still moving backward, the transition will be much less smooth, and there will unnecessary extra strain on the grip, and possibly the shoulder. The word "bouncing" suggests that this kind an abrupt transition might be happening, and that is something I want to avoid. If you feel a strong tug on your grip when you reverse the bell, this is probably happening.
I generally don't pay any attention to the angle of my torso, but let it be a proportional counterbalancing of my hip movement. Trying to keep a more upright torso may lead to abruptly and forcibly trying to resist the movement of the bell, instead of smoothly absorbing it.
All in all, it sounds like you have discovered the importance of connecting your arm to your body, but the term "bouncing" suggests that you might need to further refine your timing to smooth out the force transfer. A video might clarify whether this is true.