Please correct me if I am wrong.
Usage/Words relating to going into/out of a transport:
If going into a public transport
Take a bus/taxi
Get on [NOT into] a bus/lift; Get into a taxi
Board a bus/taxi
If going out of a transport
Take off a bus/taxi
Get off [NOT out of] a bus/lift. Get out of a taxi
Alight a bus/taxi
If all are correct, please send a message to confirm.
If any mistake, it would be very grateful if you can point it out.