주무시다 is the respectful word for sleeping, used about someone older or someone you are being polite to, and the -게 adverb in front says how. Two phrases fill these lines: 늦게 주무시다 "go to bed late," used to ask or comment about another person's hours (그때도 좀 늦게 주무셨나요?), and 편안하게 주무시다 "sleep comfortably," which shows up in well-wishes (이번 주는 꼭 편안하게 주무시길 바라겠습니다). Use 자다 for yourself and 주무시다 for the person you are addressing or talking about respectfully.