Bussen er lige ved at komme, så jeg må skynde mig til stationen.

Because bussen is the definite form, meaning the bus.

In Danish, definiteness is often shown by adding an ending to the noun:

• en bus = a bus
• bussen = the bus

So Bussen er lige ved at komme means The bus is just about to arrive / come.

The same thing happens later with stationen:

• en station = a station
• stationen = the station

This means something like is just about to come or is about to arrive.

The pattern være lige ved at + infinitive means to be just about to do something or to be on the verge of doing something.

So:

• Bussen er lige ved at komme = The bus is just about to arrive

A useful comparison:

• er ved at komme = is coming / is in the process of coming
• er lige ved at komme = is just about to come

Here lige adds the idea of just, making it feel more immediate.

Yes, in English we often say arrive, but in Danish komme is very commonly used where English would say come or arrive.

So for transport, Danish often says:

• Toget kommer snart = The train is arriving soon
• Bussen kommer nu = The bus is coming now / arriving now

You can also use ankomme in Danish, but komme is usually more natural in everyday speech.

Because these are two different grammar patterns.

In lige ved at komme, the phrase ved at is followed by an infinitive with at:

• ved at komme
• ved at gå
• ved at starte

But after a modal verb like må, Danish normally uses the bare infinitive with no at:

• jeg må skynde mig
• jeg kan komme
• jeg vil gå

So:

• er lige ved at komme → at is required
• må skynde mig → no at

Yes, må can be confusing because it can mean both may and must, depending on context.

In this sentence, it clearly means must / have to:

• Bussen er lige ved at komme, så jeg må skynde mig
  = The bus is about to arrive, so I must hurry

Why must here? Because the situation creates a necessity.

A quick comparison:

• Du må gerne gå nu = You may go now / You’re allowed to go now
• Jeg må gå nu = I must go now

So context is very important with må.

Because the verb is at skynde sig, which is a reflexive verb.

That means Danish uses a reflexive pronoun, like:

• jeg skynder mig = I hurry
• du skynder dig = you hurry
• han skynder sig = he hurries

Literally, it is something like hurry oneself, though in natural English we just say hurry.

So in your sentence:

• jeg må skynde mig = I must hurry

The mig matches the subject jeg.

Because with reflexive verbs, the reflexive pronoun usually follows the infinitive or finite verb in the normal verb phrase.

So:

• jeg skynder mig
• jeg må skynde mig
• jeg vil skynde mig

This is just the normal position for the reflexive pronoun in this kind of structure.

Because til shows movement toward a destination.

• til stationen = to the station
• på stationen = at/on the station

In this sentence, the speaker is hurrying to the station, so til is the correct choice.

Compare:

• Jeg løber til stationen = I’m running to the station
• Jeg er på stationen = I am at the station

So til is used for direction, while på is used for location.

Because the sentence contains two main clauses:

• Bussen er lige ved at komme
• så jeg må skynde mig til stationen

The comma separates those two clauses.

Also, så here means so, linking cause and result:

• the bus is about to arrive
• so I have to hurry to the station

Because så here is being used as a conjunction meaning so, joining two clauses.

After a conjunction like this, Danish keeps normal main-clause order:

• så jeg må skynde mig

If så were being used differently, or if you used an adverb like derfor (therefore), you could get inversion:

• Bussen er lige ved at komme, derfor må jeg skynde mig

So:

• så jeg må ... = normal after conjunction så
• derfor må jeg ... = inversion after fronted adverb

Yes, but the meaning changes slightly.

• Bussen er lige ved at komme = The bus is just about to come
• Bussen er ved at komme = The bus is coming / is in the process of arriving

So lige adds extra immediacy. It makes it sound as if the bus will arrive any second.

Without lige, the sentence is still correct, but it feels a little less urgent.

Yes, it sounds natural.

It uses very common everyday Danish:

• Bussen = the bus
• lige ved at = just about to
• må = have to / must
• skynde mig = hurry
• til stationen = to the station

A Danish speaker might also say similar things like:

• Bussen kommer snart, så jeg må skynde mig.
• Bussen er der næsten, så jeg må løbe til stationen.

But your original sentence is completely normal and idiomatic.