Is "While I read, the bell was ringing" correct?

Why

Sameeksha's link between "started first" and "continuous" is a reasonable guess, but the rule actually turns on a different question: which action was still GOING ON, stretched out in the background, when the second, shorter action cut into it. The reading was the longer, ongoing action — happening steadily over a stretch of time — while the bell ringing was the sudden, brief event that interrupted it at one specific moment. English marks that background, ongoing action with the continuous form ("was reading"), and the short interrupting event with the simple past ("rang"), regardless of which one technically began first in real time. Test: picture the scene — you were reading, page after page, and then, cutting into that stretch, the bell suddenly rang once — the continuous tense paints the stretched-out background, the simple past marks the sudden interruption. Her sister is right: the ongoing background action takes the continuous form ("was reading"), and the sudden interrupting event takes the simple past ("rang"), regardless of which technically started first.