You breathe it out. That is the entire answer and it is one of the most consistently surprising facts in physiology.
Fat is mostly carbon, hydrogen and oxygen. Metabolising it combines those with oxygen you inhale, and the products are carbon dioxide and water. The carbon dioxide leaves through your lungs and the water leaves as sweat, urine and water vapour in your breath.
When the proportions are worked out for a typical fat molecule, the great majority of the mass — roughly four fifths — leaves as carbon dioxide through the lungs. The remainder leaves as water.
So the lungs are the primary excretory organ for body fat. Losing weight is, quite literally, exhaling it.
Which also explains the thing that seems paradoxical about your ride: you were breathing enormously hard for twenty hours, and that heavy breathing was not merely a symptom of the effort. It was the mass leaving.