Grounding and bonding are two entirely different things. Grounding is a conductive connection between an electrical device and the ground/neutral bar in the main panel. The sole purpose for this is to carry any current from a defective electrical circuit back to the main panel. without this, you could become the conductor should, say, a pump motor hoiusing become energized.
Bonding is a process of connecting all conductive surfaces around the pool together to eliminate voltage gradients between them. We commonly refer to these voltage gradients as potentials. Everything has a certain electrical potential. Unfortunatly they all exist at different levels. Where this becoms the problem is they all want to equal out. When you are standing on, say, a concrete deck, you and the deck are at one voltage potential. When you stick your toe in the water, you become the resistive conductor to another voltage potential. If there is a big enough difference in the potential you will feel the shock. however, if we bond all of these voltage potentials together with a conductive material such as a copper wire the voltage potentials even out thus eliminating the likelyhood that you will become the conductor.
if you have an above ground pool the pump motor bond connection, the pool frame, the water and any other conductive surface within 5' of the pool edge have to be bonded together. There is also a requirement that there be a conductod burried in the ground around the perimiter if the pool.
Some areas of the country have added more to the NEC requirements and some do not even enforce it. It would be best if you spoke to the authority in your area that oversees/inspects electrical instalations to see what they require. At minimum, I would at least install up to what the NEC requires.