20 buy ins ($6000) is considered a safe bankroll. I've played with as low as 4 or 5 buy ins, but that is super risky. I just didn't have a choice.
Some players prefer more aggressive bankroll management, while others prefer to stay on the safe side. If you play a high variance style of poker or you are just starting out, it is better to have more buy ins. If you are a tighter player with a lot of experience, you could probably get away with a smaller bankroll to start.