Regarding BBB, you can learn a lot about it by looking at
The Pool Forum website. This site came from that one because The Pool Forum doesn't accept new members anymore and is not visible to Europe and Australia plus other reasons.
This post talks about BBB specifically. There are two aspects to BBB. One is that it uses store-bought chemicals that are equivalent to what is found at pool stores and mostly does this IF the store-bought version is at a lower price. The other aspect is that it focuses on using bleach or chlorinating liquid (again, whichever is less expensive for the amount of chlorine you get) as the primary source of chlorine.
The main advantages are that using bleach or chlorinating liquid results in adding only chlorine to your pool, not other chemicals. Almost every other source of chlorine adds something else to your pool. The exception is lithium hypochlorite, but that's 5 times more expensive for the same amount of chlorine (not by weight, but by how much actual chlorine gets into the pool). The other chlorine sources are Trichlor and Dichlor that both add significant amounts of Cyanuric Acid (CYA) to the pool while another chlorine source is Calcium Hypochlorite, or Cal-Hypo for short, and it adds Calcium to the pool that will raise the Calcium Hardness (CH) level. You need both CYA and CH in pools -- the issue is that these do not disappear quickly the way that chlorine does so you can end up building up these quantities too much. This all depends on how much dilution is going on in your pool such as from backwashing, rain overflow and splash-out. So by using bleach or chlorinating liquid, you can more easily maintain chemical balance by keeping CYA and CH levels in check, especially for larger pools and pools with cartridge filters.
High CYA levels, in particular, require higher Free Chlorine (FC) levels to prevent algae so typically people using Trichlor without an algaecide very often find that they get algae in their pools by the middle to end of the swimming season. You can spend more money using a weekly algaecide, but maintaining proper chlorine levels will prevent algae without any need for an algaecide. Since maintaining higher FC levels gets more costly (since about half of the FC gets used up by breakdown from sunlight on a strong summer day), using bleach or chlorinating liquid lets you keep the CYA level constant so you can keep the FC level at a lower level and therefore be able to add less chlorine daily than you would if you were using Trichlor.
The main disadvantage to using bleach or chlorinating liquid is that it is less convenient because an uncovered outdoor pool will usually need chlorine added to it every single day. With the Trichlor and Cal-Hypo products, you can get slow-dissolving tablets and these can be used in floating dispensers or in inline feeders (those two chemicals should NEVER be mixed together concentrated EVER) so may let you go several days or a week without having to manually add more chlorine. If you use a pool cover, then with bleach or chlorinating liquid you can usually go several days, so twice a week, adding more chlorine. Finally, bleach or chlorinating liquid is the least dense form of chlorine so it's heavier to carry (for the same amount of chlorine content) than other sources of chlorine.
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