Pools that meet storable classification are not required to be bonded. Your pool may fall under that classification based on how your local authority sees it.
Bonding and grounding are two often misunderstood concepts. To start, we will look at grounding first. In the 120 volt electrical supply system for your pool pump there are 3 wires. Hot, Neutral, and ground. The hot and Neutral serve to move power from the source and back to the source so the pump can run. The ground wire in this system serves only as a non resistive conductive path back to source should something happen internally in the pump. For example, if, for some reason, the hot wire came in contact with the motor housing, the housing could become energized. Without the ground present, the housing could sit there waiting to shock any unsuspecting person or animal who happened to touch it. You would be the conductor to ground. Ground being the ground you are standing on. Now, because the resistive properties of the ground you are standing on are too high for the current to short circuit back to the source, it would most likely not trip the overcurrent protection (fuse, breaker). A couple of times here I have referred to "source". This is the power company transformer on the pole out at the street. The hot and neutral connections are both on this transformer and the returning current wants to get back to what is called the center tap on the transformer either via the grounding system or the neutral system. If there is a ground wire present in the circuit, the hot wire coming in contact with the motor housing would immediately trip the overcurrent protection as there would be a dead short in the system.
Bonding. The realy mis-understood concept.
Have you ever experienced a static shock?...You know, you shuffle your feet across a carpet in the dry season and touch a metal doorknob. If you were bonded to that doorknob when you shuffled across the floor you would not have felt it when you touched it. Everything in the universe has what is refered to as electrical potential. Humans have a certain potential, a piece of steel has its own potential, water its own, etc, etc, etc. Most times this potential is not different enough to feel it. When you shufflr your feet on the carpet though your potential changes from that of the doorknob. When you get close enough to the doorknob though both you and the doorknob want to get to the same potential. when that happens, a spark jumps the gap and evens out the potential. Fortunatly there is little amperage behind it so there is no chance of geting electrocuted. Now, lets look at your pool. your pool pump is grounded back to the source thru the ground wire. But, it still is at some level of potential. Your pool water is at some other level of potential, your heater at its own level, heck, the ground you are standing on is at some level of potential. This means that all of the items in the vicinity have some varying degree of electrical potential. Under most circumstances these potentials are so close to each other that you never feel any kind of shock. however, every once in a while something happens to change the potential of one of the items. It could be a stray voltage induced from an underground electrical service, It could be a slight resistive leakage of current in your pumping system. What ever it is there is a potential difference. Now imagine you are getting out of the pool and as you touch the metal side of the pool you get the shock of your life. Hopefully not enough to kill you but a good shot none-the-less. Guess what? You just became the bonding conductor in the system. Had all of the components in the system been bonded together by the #8 bonding wire you never would have felt it. The wire is a non-resistive path between all of the components and since electricity is lazy, it will take the least resistive path. This bonding system will also protect you if you were standing on the ground and decided to touch the water to see how warm it is. If the bond is in place there would be no potential difference between the water and the ground even if there were a stray current floating around.
Hopefully this helps clear some of this up