Your question can be answered by first looking at what happens in ocean basins. Due to the fact that Earth rotates, the water in the ocean basins moves form the west towards the east. When this happens, the water on the surface of the ocean also moves from west to east. In the Pacific, this causes the surface waters off of the coast of CA to move out to sea. The displaced water is replaced with deeper water that is rich in sediments and nutrients. The sediments and organic material are the main causes of the cloudy water along the CA coast. The Bahamas and Hawaii do not experience the degree of upwelling our coast does. They are also protected in many areas by reefs which cause their shorelines to be less energetic. The amount of energy the water has helps to dictate its sediment load. I hope that this answers your question.

There are several things that can cause water to be unclear, or turbid. Perhaps the two most common culprits for turbid water are:

1) suspended or stirred-up sediments,
2) living organic material, such as phytoplankton.

The suspended sediments may arise from either water action due to storm swells or waves, or from sediments carried into the ocean from rivers, especially during periods of heavy storm run-off. The organic material typically consists of phytoplankton and/or zooplankton that bloom when light is made available during the spring, summer, and fall and when nutrients are made available by processes such as upwelling or vertical mixing during storms.

The reason that the water in the Bahamas and Hawaii is clearer than along the California coast is likely a combination of both of these factors: 1) the sediments in the Bahamas and Hawaii tend to be composed of heavier particles that are not as easily stirred up or suspended, and 2) there tends to be far less phytoplankton and zooplankton in the water due to very low nutrients in the Bahamas and Hawaii.

Along the California coast, much of the soft sediment is composed of very fine sand, mud, or silt, all of which are quite easily stirred up. Mud and silt, when stirred up, can remain suspended in the water column for many hours, even days, causing the water to be quite unclear after storm action stirs up the bottom or heavy river run-off deposits sediments into the water. I have been diving in places where the silt has been stirred up on the bottom at 100 feet depth by a violent storm one or two weeks prior, and the visibility was still less than 1 foot at the bottom. I am not sure what the origins of these sediments are.

In contrast, in Hawaii and the Bahamas, the sediments are mostly heavy, coarse-grained sands that are largely composed of eroded remnants of dead coral skeletons, calcareous algae, mollusk shells, and the limestone islands themselves (in the Bahamas). These heavy sands are not easily stirred up or suspended in the water column except during large tropical storms or hurricanes. It is not necessarily true that these locations experience less wave action than California, as anyone living on the North Shore of Oahu or who has been through a tropical storm or hurricane in the Bahamas can surely attest. However, Hawaii and the Bahamas do require more wave action to stir up their sediments than in California, and when the sediments are stirred up they typically remain suspended for a shorter period of time . I was once diving on a shallow reef in the Bahamas when a thunderstorm swept overhead us. The water was very clear before the storm came, but the strong winds from the storm caused local wind waves and wind-driven currents to stir up the bottom and we were soon in the middle of an underwater white-out, with sand swirling all around us. Much of the sand settled back down after the storm passed, though, and the visibility improved somewhat.

The other cause for turbidity is living organic material in the water; it is also an important reason that California water is less clear than Hawaiian or Bahamian waters. The waters off California typically have much more phytoplankton and chlorophyll, and therefore are more turbid, than in Hawaii or the Bahamas. This is because the waters in California are very nutrient rich in comparison to the waters in Hawaii or the Bahamas (or much of the rest of the tropics). Nutrients are typically depleted in the surface waters due to photosynthesis and are abundant in deeper waters where they are replenished by the decay and biodegrading of organic matter that sunk into the ocean depths. The nutrients however, usually have a hard time mixing back into the surface waters because there is a boundary layer below the surface caused by an abrupt increase in density, called the pycnocline, which prevents water from mixing vertically.

The pycnocline (the layer of density change) is usually very deep and pronounced in Hawaii and the Bahamas due to a very warm surface layer, thereby trapping nutrients in deeper waters that do not receive enough light for phytoplankton to grow. Therefore, there is very little chlorophyll in these tropical waters, keeping them clear. (As an aside, corals are symbioses where phytoplankton have evolved to survive in nutrient-poor tropical waters by living inside the bodies of the corals and obtaining nutrients directly from the waste products of the corals. The energy that the phytoplankton capture during photosynthesis is then passed onto the corals). In California, the pycnocline is shallower and weaker because the cold California Current keeps the surface layers cool.