Getting your horse on the bit means that the horse is carrying itself with a rounded frame and accepting contact with the rider's hands. This creates a connection between the horse's hindquarters and its front end, allowing for better balance and responsiveness.
Some bits are made with different types of metal to be "sweet" and to encourage salivation, as this makes the horse accept the bit and relax to it. If your horse is dribbling or drooling, your bit could be one of these. If he is foaming at the mouth after a long workout, that is just another type of sweat and is normal. All in all, salivation doesn't have to be a bad thing, but if you don't like it, go to your saddle shop and ask for a bit that hasn't been sweetened.
The bit is something that goes in the horses mouth so the rider can steer the horse. So free from the bit probably means that the bit fell out of the horses mouth.Wikipedia can tell you more: http://en.wikipedia.org/wiki/Bit_(horse)
If you mean the Horse Whisperer, he is a bit south of the docks on the fringe of the jungle.
It is typically an aerated liquid.
Most likely cause is that is was poisoned. Or a respiratory problem.
This is a horse term. A horse that is eager to move will chew or chomp at the bit in its mouth, and pull on the reins to try to get the rider to let him move. If you are chomping at the bit, you are eager to get started on something.
The device placed in a horse's mouth is called a bit. It is part of the bridle and is used to communicate with the horse while riding by providing cues and signals.
Above the means the horse is avoiding the pressure and may grab the bit with his tetth and take off.
Plant foaming and polymer foaming
A bit lifter is a piece of horse tack which lifts a bit in the horse's mouth.
I'm not familiar with a 'headpiece' but I think you mean the bridle. This is used to control the horse's head and keeps the bit in the horse's mouth.