Автобус едет через мост к центру.

Russian normally uses идти for going on foot and ехать for going by vehicle.

So:

• человек идёт = a person is walking
• автобус едет = a bus is going / moving

Because the bus is traveling as a vehicle, едет is the expected verb here.

You may sometimes hear автобус идёт in real speech, especially when talking about a route or service, like the bus goes/runs, but едет is the basic literal choice for a bus in motion.

Едет is the 3rd person singular present form of ехать.

Russian present tense often covers both:

• English goes
• English is going

The exact English translation depends on context.

In this sentence, the bus is pictured as moving right now, so English naturally uses is going or is driving / is traveling.

If you wanted a habitual meaning, Russian would more likely use ездит:

• Автобус ездит к центру = the bus goes to the center regularly

The preposition через takes the accusative case.

So мост here is accusative. But мост is a masculine inanimate noun, and in the singular, masculine inanimate nouns often have the same form in the nominative and accusative.

That is why you see:

• nominative: мост
• accusative: мост

So the form does not change, even though the case has changed.

Both can be possible, but they are not exactly the same.

• через мост emphasizes crossing from one side to the other by means of the bridge
• по мосту emphasizes movement along/on the bridge itself

In this sentence, the idea is that the bus goes across the bridge on its way toward the center, so через мост is very natural.

Also, the case changes with the preposition:

• через мост → accusative
• по мосту → dative

Because the preposition к requires the dative case.

The noun центр changes in the dative singular:

• nominative: центр
• dative: центру

So:

• к центру = toward the center

This is just normal case government: к + dative.

They are close, but the nuance is different.

• к центру = toward the center, in the direction of the center
• в центр = into the center / to the center, with a stronger sense of entering or reaching it

So к центру is a bit more directional, while в центр sounds more like the center is the destination itself.

In many real situations, both could be possible, but they do not feel exactly identical.

Russian has no articles.

So автобус can mean:

• the bus
• a bus

And the same is true for мост and центр.

Russian leaves that information to context instead of using separate words like English the and a.

Yes. Russian word order is much more flexible than English word order because case endings help show the grammatical relationships.

The sentence as given:

Автобус едет через мост к центру.

is a neutral, natural order.

But you could move parts around to change emphasis:

• К центру автобус едет через мост.
  Focuses more on the destination.

• Через мост автобус едет к центру.
  Focuses more on the route.

The meaning stays very similar, but the emphasis shifts.

In a transport or city context, центр usually means the city center or downtown, not the geometric center of something.

So к центру would usually be understood as toward downtown / toward the city center.

Автобус is a masculine noun, but in the present tense, the verb едет does not show gender.

Here, едет only tells you that the subject is:

• 3rd person
• singular

Gender would matter in the past tense:

• автобус ехал = the bus was going

So in this sentence, gender belongs to the noun, but it does not change the present-tense verb form.