Running water through a filter sock and changing every 24 hrs is generally effective. Additionally, as you know, this is part of the nitrogen cycle and likely as you stated keeping it simple, the bacteria is growing so rapidly that collectively they become visible to the naked eye, causing the water to become milky/cloudy/hazy in appearance. Its likely the Heterotrophic Bacteria, which is the bacteria that cannot synthesize its own food and is dependent on complex organic substances for nutrition. The heterotrophs in the aquariums mineralize the organic waste (break down the uneaten food, fish waste, dead plant matter, etc. into ammonia). Also, it is more common that the heterotrophs are seen in bacterial blooms, not the trusted autotroph nitrifiers.
In a newer setup, the heterotrophs get to work quicker than the autotrophs, causing the "cycling bloom" so often seen. Blooms are almost certainly heterotrophic if they are caused by a build-up of organic waste in the substrate, which most, if not all, are.
Bacterial blooms are common in tanks with apparently no organics present (for example, where all that is in the tank is water and ammonia for a fishless cycle). This is caused by the dechlorination of the water suddenly enabling the water to support bacterial populations. The heterotrophs immediately get to work on the organics in the water itself.
