Nine Arch Bridge itself is free and open all day, a short walk or tuk-tuk ride from Ella town. But the reason most people go — a train crossing the viaduct — only happens a few times a day, and the schedule shifts occasionally.
The most reliable slots are the mid-morning and late-afternoon trains, roughly matching the Badulla-Colombo line timetable, but confirm the current schedule locally the day before rather than trusting an old blog post (this one included).
Arrive at least 30 minutes early for a good vantage point. the surrounding cafes with elevated decks fill up fast, and the classic shot from the tea-field side gets crowded closer to train time.