Rasulullah (ﷺ) used to say Bismillah while boarding the ride, he said the rest of the dua after getting up:

اَلْحَمْدُ لِلَّهِ، سُبْحَانَ الَّذِي سَخَّرَ لَنَا هَذَا وَمَا كُنَّا لَهُ مُقْرِنِينَ وَإِنَّا إِلَى رَبِّنَا لَمُنْقَلِبُونَ، اَلْحَمْدُ لِلَّهِ، اَلْحَمْدُ لِلَّهِ، اَلْحَمْدُ لِلَّهِ، اَللَّهُ أَكْبَرُ، اَللَّهُ أَكْبَرُ، اَللَّهُ أَكْبَرُ، (لَا إِلَهَ إِلَّا أَنْتَ) سُبْحَانَكَ، إِنِّي ظَلَمْتُ نَفْسِيْ فَاغْفِرْ لِي فَإِنَّهُ لَا يَغْفِرُ الذُّنُوْبَ إِلَّا أَنْتَ

Alhamdu lillaah. Subhaanal-ladhee sakhkhara lanaa haadhaa wa maa kunnaa lahu muqrineen. Wa 'innaa 'ilaa Rabbinaa lamunqaliboon. Alhamdu lillaah, alhamdu lillaah, alhamdu lillaah, Allahu 'Akbar, Allahu 'Akbar, Allahu 'Akbar, (laa ilaaha illaa 'Anta) subhaanaka 'innee dhalamtu nafsee faghfir lee, fa'innahu laa yaghfirudh-dhunooba 'illaa 'Anta

Praise is to Allah. Glory is to Him Who has provided this for us though we could never have had it by our efforts. Surely, unto our Lord we are returning. Praise is to Allah.(3 times) Allah is the Most Great. (3 times) Glory is to You. O Allah, I have wronged my own soul. Forgive me, for surely none forgives sins but You.

Reference: Sahih. Tirmidhi: 3446