Je suis obligé de prendre le premier bus pour arriver à l'heure au travail.

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

• être obligé de + infinitive means to be obliged / forced / required to do something
• devoir + infinitive means to have to / must do something

In this sentence, je suis obligé de prendre... suggests a stronger sense of necessity, often because of circumstances.

Compare:

• Je dois prendre le bus. = I have to take the bus.
• Je suis obligé de prendre le bus. = I’m obliged / forced to take the bus.

So être obligé de can sound a little stronger or more constrained than devoir.

Obligé agrees with the speaker.

• If the speaker is male, it is obligé
• If the speaker is female, it is obligée

So:

• Je suis obligé de... = said by a man
• Je suis obligée de... = said by a woman

This is because obligé is an adjective used with être, and French adjectives usually agree in gender and number.

Because the pattern is:

• être obligé de + infinitive

So when you want to say someone is obliged to do something, you use de before the infinitive verb.

Examples:

• Je suis obligé de partir.
• Elle est obligée de travailler.
• Nous sommes obligés d’attendre.

This is just the normal construction you have to learn with obligé.

In French, the normal expression is prendre with forms of transport:

• prendre le bus
• prendre le train
• prendre le métro
• prendre un taxi

French does not usually use a direct equivalent of English ride the bus in this context.
So prendre is the natural verb here, even though it literally often means take.

Le premier bus means the first bus.

French often uses the definite article when referring to something specific or understood in context. Here, it means the first bus available in the schedule or the first bus of the day that matters to the speaker.

• le premier bus = the first bus
• un premier bus would usually not sound right here

Un premier is possible in some other contexts, but in this sentence, le premier bus is the normal choice.

Here, premier means first in an ordered sequence.

So le premier bus is the earliest bus, or the first one available according to the schedule.

A useful point:

• premier / première = first
• It agrees in gender:
  • le premier bus
  • la première fois

Since bus is masculine, it is premier.

Pour + infinitive is often used to express purpose: in order to, so as to.

So:

• pour arriver à l’heure = in order to arrive on time

This explains why the speaker has to take the first bus.

A very common pattern in French is:

• Je travaille pour gagner de l’argent.
• Elle part tôt pour éviter la circulation.
• Nous prenons le métro pour aller plus vite.

Because the correct expression is à l’heure.

• à l’heure = on time
• en retard = late

So you say:

• arriver à l’heure
• être à l’heure
• partir à l’heure

The à is part of the fixed expression. You cannot leave it out.

À l’heure is the normal expression for on time.

• Je suis à l’heure. = I am on time.
• Il est arrivé à l’heure. = He arrived on time.

En heure is not the normal phrase for this meaning in standard French. So in this sentence, à l’heure is the correct expression.

Because au is the contraction of à + le.

• à + le = au
• à + les = aux

Since travail is masculine singular, French uses au travail.

Examples:

• Je vais au travail.
• Il est au bureau.
• Nous parlons aux enfants.

So au travail literally comes from à le travail, but French contracts it to au.

In this sentence, au travail is best understood as to work in English because it depends on arriver:

• arriver au travail = to arrive at work

So grammatically, it means at work, but in natural English we usually say arrive at work.

French and English organize this idea differently.

French says:

• au travail = literally at the work

But English usually says:

• at work

This is very common: French often uses an article where English does not.

Other examples:

• à l’école = at school
• à la maison = at home
• à la banque = at the bank

So even if English drops the article, French may still need one.

Yes, but pour is much more common in everyday French.

• pour arriver à l’heure = normal, natural, common
• afin d’arriver à l’heure = more formal, more written

Both are correct. In conversation, pour is usually the better choice.

This is because of how French handles de before a vowel sound.

• obligé de prendre → no contraction needed, because prendre starts with a consonant
• afin de arriver becomes afin d’arriver → de shortens to d’ before a vowel

The same thing would happen with obligé if the next verb started with a vowel:

• Je suis obligé d’attendre.
• Elle est obligée d’y aller.

So de becomes d’ before a vowel or mute h.

You would change both the subject and the agreement:

• Nous sommes obligés de prendre le premier bus pour arriver à l’heure au travail.

If the group is all female, it would be:

• Nous sommes obligées de prendre le premier bus...

So with être obligé, the adjective still agrees with the subject.

Yes, it is natural and correct.

It sounds like normal spoken or written French. It clearly expresses:

• necessity: je suis obligé de
• the action: prendre le premier bus
• the purpose: pour arriver à l’heure
• the destination/context: au travail

A native speaker might also say:

• Je dois prendre le premier bus pour être à l’heure au travail.

That version is also natural, but the original sentence is completely idiomatic.