A bull market is a sustained period of rising prices in an index or a market, conventionally described as beginning once prices have risen roughly 20 percent from a recent low and continuing until they have fallen roughly 20 percent from a subsequent high. The threshold is not purely editorial: the Securities and Exchange Commission's own investor glossary describes a bull market as a time when stock prices are rising and sentiment is optimistic, occurring "generally" when there is a rise of 20 percent or more in a broad market index over at least a two-month period. That is investor education rather than a rule, it appears nowhere in the Code of Federal Regulations, and it says nothing about when a bull market ends. The end condition above is the commentators' convention rather than the regulator's, and both the start and the end still depend on choices someone has made about which index to use and which low to measure from.
The two labels are defined against each other, which produces an awkwardness worth noticing. A bull market conventionally starts at the low point that ended the previous decline, but that point is only identifiable once prices have risen enough to make it a low. The start date is therefore assigned backward from a threshold crossed later. It is a real description of what happened; it is not a signal that existed at the time.