Learn Hardcore Russian: Я еду на машине по дорожному мосту.

It indicates the means of transportation—in this case, that the speaker is traveling by car. In Russian, when referring to vehicles as a means to get somewhere, the fixed expression “на машине” is used.

Which case is used for машине in “на машине” and why?

The word машине is in the prepositional case. Although one might expect the instrumental for expressing the means of travel, the conventional, idiomatic usage for vehicles in expressions like “на машине,” “на автобусе,” or “на поезде” employs the prepositional form.

What role does the preposition по play in “по дорожному мосту”?

The preposition по expresses movement along or over a surface. In this sentence, it indicates that the speaker is driving along (or over) a bridge. Because по in such contexts governs the dative case, “дорожный мост” becomes дорожному мосту.

Why is the adjective transformed into дорожному instead of its base form дорожный?

Since the preposition по requires the noun “мост” to be in the dative case (yielding мосту), the adjective must agree with it. Therefore, дорожный is inflected into the dative masculine form дорожному.

Why is the verb ехать used rather than идти in this sentence?

The verb ехать is used when referring to movement by a vehicle, whereas идти is reserved for walking. Because the context involves traveling by car, ехать is the appropriate choice.