Dua when boarding a vehicle

When. As you settle into the seat — after mounting, not while still standing beside it. It applies to whatever carries you: a car, a bus, a plane, a bicycle. The travel supplication that follows, asking for righteousness and ease on the journey, comes after this one.

The words. Sakhkhara is the verb worth pausing on. It means to subject something, to press it into service, and its root carries the sense of a thing made to work without being able to refuse. Its object here is hadha, 'this' — the specific vehicle under you, not transport in general. The middle words of the sentence are Qur'anic, from az-Zukhruf (43:13), where they are given as what one says on mounting: subhana alladhi sakhkhara lana hadha wa ma kunna lahu muqrinin, 'we could never have brought it under control ourselves'.

Why glorification rather than a request. The three openings — bismillah, alhamdulillah, subhanallah — are naming, thanking and declaring transcendence, in that order. No request has been made yet. The moment being marked is not the danger of travel but the strangeness of an animal or a machine carrying a human being at all.

What muqrinin adds. The Qur'anic phrase says the riders were never muqrinin — never a match for it, never able to hold it. Anyone who has felt a vehicle slide, or an animal refuse, knows the claim is literal. The subjection is on loan.

A note. Nothing in it is specific to camels or horses. The word hadha takes whatever you are sitting in.