Explanation
We use by when we talk about “means of transport”.
We use by bicycle, by car, by taxi, by bus, by train, by boat, by ship, by plane, by air & by sea.
We travel by bus.
“On” is used with a specific bicycle, bus train, ship plane.
Come on my bicycle.
“In” is used with a specific car, taxi, van, lorry & ambulance.
Note: “By” is not used when we refer to a specific bicycle/car/train i.e. means of transport.
She went there on my bicycle/bike.
He went there in your car.
They came in a taxi.
They will go on the 9:30 bus.
Note: We say “On Foot”.
She goes to school on foot.