The easyJet plane, which departed Gatwick at 7.35am, was diverted to Edinburgh after weather forced the crew to abandon a landing attempt at Glasgow.
After flying east, a second landing attempt in Edinburgh was aborted as the storm reached the Scottish capital.
Hazel Bedford, a Cancer Research UK worker, who was flying to Glasgow for a mid-morning meeting, said: "I'm feeling really lucky to be alive.
"We took off as normal, the captain came over the PA and said there was a chance it could be a bit bumpy north of the Border and there could be some delays while landing.
"But we got further north and suddenly everything started shaking and bumping, we were going up and down, up and down, like a roller coaster. It looked like we were going to land as normal and were just above the buildings when we were suddenly in full climb again."
Ms Bedford explained that the crew said they would travel to Edinburgh, where weather conditions were believed to be better.
She said: "We came into land in Edinburgh and again the same, it felt like we we're hitting big air pockets and dropping huge distances.
"An awful lot of people were being sick but the plane, it was incredibly quiet.
"All I could think of was my new year's resolution, which was to write my own will, and I haven't done it. It was that frightening. I was absolutely terrified."