What's a good bounce rate and how do I keep mine low?

Generally, under 2% is considered healthy, 2–5% is a warning sign worth investigating, and above 5% is a real deliverability risk that ISPs will start noticing. At 3% you're in the “keep an eye on it” range. The most effective way to keep it low is verifying emails before you send to them (there are email verification services that check deliverability without actually sending) and removing hard bounces from your list immediately rather than retrying them.