Skulle bussen være forsinket igjen, kan hun jobbe hjemme den første timen etter avtale med sjefen.

This is a conditional clause without hvis. Norwegian can leave out hvis and put the verb first instead:

• Hvis bussen skulle være forsinket igjen, ...
• Skulle bussen være forsinket igjen, ...

Both mean roughly if the bus should be delayed again.

This verb-first pattern is a bit more formal or written in style, and it is common in Norwegian in conditional sentences.

Not really. Although skulle is formally the past tense of skal, here it is being used in a conditional / hypothetical way.

So in this sentence, skulle does not mainly refer to past time. Instead, it gives the sense of:

• if it should happen that ...
• in the event that ...

So Skulle bussen være forsinket igjen means something like Should the bus be delayed again or If the bus happens to be delayed again.

Because skulle is the finite verb here, and the next verb stays in the infinitive:

• skulle være
• kan jobbe

This is normal with modal verbs in Norwegian. Compare:

• Hun kan jobbe = she can work
• Bussen skulle være forsinket = the bus should be delayed / were to be delayed

So være is infinitive because it depends on skulle.

Yes, but it is a little more formal or written than the most neutral everyday version.

Common alternatives are:

• Hvis bussen er forsinket igjen, ...
• Hvis bussen skulle være forsinket igjen, ...

The version in your sentence has a slightly more careful, conditional tone, similar to English Should the bus be delayed again.

Here igjen means again.

So:

• forsinket igjen = delayed again

It suggests that this has happened before, and the speaker is talking about a repeated possibility.

Be careful: igjen can also mean back in other contexts, but here it clearly means again.

This is because Norwegian follows the V2 rule in main clauses: the finite verb usually comes in the second position.

The first part of the sentence is a fronted conditional clause:

• Skulle bussen være forsinket igjen, ...

After that comes the main clause, where the finite verb must come before the subject:

• kan hun jobbe hjemme ...

So this is normal Norwegian word order. Compare:

• Hun kan jobbe hjemme.
• Hvis bussen er forsinket igjen, kan hun jobbe hjemme.

Once another element comes first, kan moves before hun.

Because hjemme means at home, while hjem usually means home as a destination.

Compare:

• Hun er hjemme. = She is at home.
• Hun drar hjem. = She goes home.

In your sentence, she will work at home, so hjemme is the correct word:

• jobbe hjemme = work from home / work at home

Den første timen means the first hour.

In Norwegian, when you have an adjective before a definite noun, you often get double definiteness:

• den første timen
• literally: the first hour

Here:

• første = first
• timen = the hour
• den marks definiteness together with the ending on timen

This is very common in Norwegian:

• den store bilen = the big car
• det nye huset = the new house

Because timen is the definite singular form of time.

• en time = an hour
• timen = the hour

Since the phrase means the first hour, Norwegian uses the definite form:

• den første timen

It means something like by arrangement with the boss, as agreed with the boss, or by prior agreement with the boss.

The phrase etter avtale med ... is a common expression meaning that something happens because there is an agreement or permission in place.

So here it suggests that working from home for the first hour is possible if this has been agreed with her boss.

Because sjefen already contains the definite article as an ending.

• en sjef = a boss
• sjefen = the boss

Norwegian usually puts the definite article at the end of the noun, not as a separate word like English the.

So:

• med sjefen = with the boss

Yes. Bussen is the definite form:

• en buss = a bus
• bussen = the bus

So it normally refers to a bus that is already known from the situation or context, for example her usual bus.

The comma separates the conditional clause from the main clause:

• Skulle bussen være forsinket igjen,
• kan hun jobbe hjemme ...

This is very natural in writing, especially when the sentence begins with a longer subordinate or conditional element.

Yes. Kan often corresponds to both can and may, depending on context.

Here it probably means something between:

• she can work from home
• she is allowed to work from home

Because the sentence ends with etter avtale med sjefen, the idea of permission / arrangement is important, not just ability.

It is mostly neutral, but the opening Skulle bussen være ... gives it a slightly more formal or written feel than everyday casual speech.

In more everyday spoken Norwegian, many people would say something like:

• Hvis bussen er forsinket igjen, kan hun jobbe hjemme den første timen etter avtale med sjefen.

So the grammar in your sentence is perfectly normal, but the style is a bit more polished.