Are three bites in a row always bed bugs?

No. Three bites in a row do not prove that bed bugs are responsible. Bed bug bites can appear in a line or an irregular pattern, and other insect bites or skin conditions can look similar. Counting marks is not a reliable way to confirm an infestation. (CDC: Bed bugs; EPA: How to find bed bugs)

Check the sleeping area for physical evidence, such as live bed bugs, shed skins and dark spotting in mattress seams or bed-frame cracks. A confirmed insect identification is more useful than a bite photograph. If you cannot find pest evidence, keep other possible causes in mind instead of treating the pattern as a diagnosis. (EPA: How to find bed bugs)