Some people want a bankroll for psychological reasons. If you need 100 buy-ins to be able to play your A-game, then you better have 100 buy-ins.
However, there is another very real reason to need a bankroll, and that is to weather the downswings which will occur. The downswings depend on your win rate. If your win rate is half that of another player's, or your win rate at a lower level, then you will see downswings which are twice as large, so you need twice the bankroll to be as safe. You NEED to know your win rate to know how large the downswings will be. Other people can tell you about their win rates, but not yours. If you don't know that you are a winning player at all, you need to set a budget for poker rather than thinking about bankroll management.
A good bankroll formula is
bankroll = comfort * SD^2 / WR
where comfort depends on your risk tolerance and ability/willingness to move down. A comfort level of 2 is aggressive. A comfort level of 4 is conservative. SD is your standard deviation, which is reported by programs like PokerTracker and Hold'em Manager, and it is typically about 90 big blinds/100 hands for 6-max players who buy in full, but it depends on playing style. WR is your win rate. For example, if you use a middle-of-the-road comfort level of 3, and your SD is 90 big blinds/100 hands, and your win rate is 6 big blinds/100 hands, then your bankroll should be about
3 * 90^2 / 6 = 4050 big blinds = 40.5 buy-ins.
If your win rate is only 3 big blinds/100, then you need twice as many, or 81 buy-ins.
If your bankroll drops below this amount, it doesn't mean you have to stop. However, playing with less than half of the recommended bankroll should be viewed as an expense.