It's WAY too much to type here. I suggest you access the UC Davis website on their winemaking course. You'll have a real appreciation for all the chemical changes that take place during bulk aging---it's more than just clearing a wine!!!! But I'll give a small over-view below.
How to know when to bottle---this why bulk aging is so important. So many people on wine forums talk about stabilizing wine. Most of the time, they are alluding to using sorbate. But the real secret is that when you are bulk aging THAT is stabilizing a wine. Haze, precipitates, and sediments form colloides and then form large agglutinated complexes. Given enough time for these polymerzation and agglutination reactions to take place, the particulate matter drops out and can be removed thru racking. This removes these unstable components from the wine, thus stabilizing it. Now there are conditions that depend on this happening in any given time frame. But essentially, 1 to 1 1/2 years is the time frame we always work with.
Aging also gets rid of unwanted esters that may form due to microbes, which are also unstable. Given time, these dissipate and improve the wine too. Plus, aging stabilizes tannins, pigments and color. Bitter or astringent compounds form large clusters and drop out too.
Yes, juice has less debris in it as far as clearing goes. But as you see---bulk aging isn't just about wine being clear.
Cold stabilization depends on the use of carbonate. Usually potassium carbonate. If you are using calcium carbonate to increase PH, it will drop out the acids at room temp. And also--believe it or not, CS depends on PH and is used more for acid reduction than clearing. I'm not a fan of CS for any reason other than acid reduction, but agree that if you use bentonite in the secondary and still have cloudy wine after a few months, some chilling of the wine seems to aid in clearing. Cool temps are better for wine storage than warm temps--so that right there is a good reason for storing the wine in the root cellar.