Learn Hardcore Turkish: Otobüsü durdurmak için düğmeye basıyorum. - I am pressing the button to stop the bus.

Because it is the definite direct object of durdurmak (to stop something). In Turkish, definite direct objects take the accusative suffix -(y)I. Since the last vowel of otobüs is ü, the accusative becomes otobüsü. If it were indefinite (a bus), you would normally leave it bare: otobüs (e.g., otobüs durdurmak = to stop a bus, in general).

Why is it düğmeye (dative -e) and not düğmeyi (accusative)?

The verb basmak takes the dative when it means “to press” or “to step on.” Think of it as “press to the button.” So you say düğmeye basmak. Using the accusative (düğmeyi) would be ungrammatical in this sense.

What’s the difference between durmak and durdurmak?

durmak = to stop (intransitive; the subject stops by itself): Otobüs durdu (The bus stopped).
durdurmak = to make something stop (transitive causative): Otobüsü durdurdum (I stopped the bus).
Here, durdurmak is formed from dur-
- causative -dur
  - infinitive -mak.

How is the present continuous basıyorum formed?

It’s root bas- + present continuous -iyor (harmonized) + 1st person singular -um:

bas- + -ıyor + -um → basıyorum
The -iyor set harmonizes as -ıyor/-iyor/-uyor/-üyor depending on the last vowel of the root. With a in bas-, you get -ıyor.

Why is the subject pronoun ben missing?

Turkish is pro-drop: the person/number on the verb (-um in basıyorum) already shows the subject, so ben is optional. You could say Ben düğmeye basıyorum, but it’s only needed for emphasis or clarity.

Could I use the aorist or future instead of the present continuous?

Yes, but the meaning changes:

Basarım (aorist) = I press/I tend to press (habitual/general).
Basıyorum (present continuous) = I’m pressing (right now/around now).
Basacağım (future) = I will press (later/soon).
In your sentence, basıyorum fits a current action.

Can I change the word order?

Yes. Turkish is flexible, but the default is object–verb. Common variants:

Otobüsü durdurmak için düğmeye basıyorum (neutral, purpose up front).
Düğmeye, otobüsü durdurmak için basıyorum (focus on where you press).
Otobüsü durdurmak için basıyorum düğmeye (colloquial, end-focus on the button).
Keep the object before its verb inside the infinitive phrase: otobüsü durdurmak is more natural than durdurmak otobüsü.

Is otobüsü durdurmak a separate clause?

It’s a non-finite (infinitive) purpose clause: [otobüsü durdurmak] için modifies the main clause düğmeye basıyorum. The object otobüsü belongs to durdurmak, not to basıyorum.

What exactly does için do here?

için means “for” or “in order to.” With a verb in the infinitive (-mak/-mek), it expresses purpose: V-mak için = in order to V.
It also works with nouns: otobüs için = for the bus (not necessarily “to stop the bus,” just “for the bus” in general).

Could I say Otobüs için düğmeye basıyorum?

That means “I’m pressing the button for the bus” (for the sake of the bus), which is ambiguous and does not clearly state the purpose “to stop the bus.” To express purpose, keep V-mak için: Otobüsü durdurmak için…

Is there an alternative to -mak için for purpose?

Yes:

Nominalized clause: Otobüsün durması için düğmeye basıyorum (I’m pressing the button so that the bus stops).
With diye
- a finite verb: Otobüsü durdurayım diye düğmeye basıyorum (I’m pressing the button so that I may stop the bus).
  All are correct; -mak için is the most straightforward.

How do I say it in the past?

Simple past: Otobüsü durdurmak için düğmeye bastım (I pressed the button to stop the bus).
Past continuous: … düğmeye basıyordum (I was pressing…).
Narrative variants are possible depending on context.

Why is it otobüsü with ü, not otobusu?

Vowel harmony. The accusative suffix is -(y)I, where I becomes ı/i/u/ü based on the last vowel of the stem. The last vowel of otobüs is ü, so the suffix surfaces as -ü: otobüs + -ü → otobüsü.

What’s going on with the letter ğ in düğmeye?

That’s yumuşak g. It isn’t pronounced like a hard g; it lengthens or glides the preceding vowel. düğme is roughly like “duüme,” and düğmeye adds the dative -e with a buffer -y- because the word ends in a vowel: düğme + (y)e → düğmeye.

Could I say zile basıyorum instead of düğmeye basıyorum?

Yes, very natural on buses. Zil is “bell,” and zile basmak is idiomatic for “press the stop button/ring the bell.”

Why not just use durmak in the purpose clause?

Because the intention is to make the bus stop (a caused action). Otobüsü durdurmak expresses causing the bus to stop. Durmak için düğmeye basıyorum would mean “I’m pressing the button to stop (myself),” which doesn’t match the bus context.

Is there any article like “the” in Turkish?

No separate articles. Definiteness is often shown by context and case marking. Using the accusative (otobüsü) strongly signals a definite object (the bus). Without it (otobüs), the object is typically indefinite or generic.