Running a Live Whiteboard Sketching Exercise

In an on-site interview, you're handed a marker and asked: "Sketch the flow for a user booking a one-way flight, right now, on this whiteboard." No further detail is given.

1. Describe, step by step, how you'd open this exercise in the first 30 seconds — what you'd say and draw first, and why in that order.
2. The prompt doesn't specify whether the user already has an account, is searching from a homepage, or has a specific date in mind. How should you handle that ambiguity live, and why is that approach stronger than either guessing silently or asking to pause until every detail is specified?
3. Partway through, the interviewer says "actually, assume the user also wants to add a checked bag." How should you incorporate this without erasing and restarting?