Less than most people think. A rebound net sends the ball back towards the player, so the space you need is mostly in front of it.
The short answer
For passing, allow about four metres in front of the net and a metre either side. For setting, add height rather than length: a clear three metres above the player.
Surfaces
Grass is forgiving and quiet. A driveway or patio gives a truer bounce but is harder on knees, so wear pads for any floor work.
Neighbours
The ball is quiet on a tensioned net. The noise people notice is the ball landing, which a lawn absorbs far better than paving.