Answer: Twice
The first time Ian sees Toula, at Dancing Zorba's, she is so entranced with him she can barely move. Ian is polite but indifferent. He sees her the second time while buying a hot dog outside the travel agency owned by her aunt. Ian waves and Toula freezes. When he turns away, she ducks behind a water cooler. The third time he sees her, while passing her aunt's travel agency, he finally goes inside and asks her out.