Vi blev snabbt överens om att ta bussen istället.

Because blev is the past tense of bli, which means become. The expression bli överens means to come to an agreement or to reach agreement.

So:

• Vi blev överens = We came to an agreement
• Vi var överens = We were in agreement

The first one focuses on the change or result of a discussion. The second one just describes the state.

In this sentence, the idea is that they reached agreement quickly, so blev is the natural choice.

Överens means in agreement, agreed, or of one mind.

It is very commonly used in expressions like:

• vara överens = to be in agreement
• bli överens = to come to an agreement
• komma överens = to agree / come to an agreement

You will often see it followed by:

• om + noun
• om att + infinitive
• sometimes med + person

Examples:

• Vi är överens om planen. = We agree about the plan.
• Vi blev överens om att vänta. = We agreed to wait.
• Jag är överens med henne. = I agree with her.

After överens, Swedish often uses om to introduce what the agreement is about.

Here, the structure is:

• överens om att + infinitive

So:

• överens om att ta bussen = agreed to take the bus

This is a very common pattern in Swedish:

• Vi blev överens om att gå hem. = We agreed to go home.
• De är överens om att börja tidigt. = They agree to start early.

You can think of om here as linking the agreement to its content, and att ta bussen gives the action.

Here, att is the infinitive marker, like to in English.

So:

• ta = take
• att ta = to take

In om att ta bussen, the att belongs with the verb ta. It is not the conjunction that here.

So the sentence does not mean something like about that take the bus. It means about taking the bus or to take the bus.

Swedish often uses the definite form with common means of transport after verbs like ta:

• ta bussen = take the bus
• ta tåget = take the train
• ta bilen = take the car

Even when English uses the bus in a general way, Swedish also usually uses the definite form.

Compare:

• ta bussen = take the bus
• åka buss = go by bus / travel by bus
• ta en buss = take a bus, one bus, some bus

So bussen here is completely normal and idiomatic.

Istället means instead.

At the end of the sentence, it modifies the whole action:

• ta bussen istället = take the bus instead

This means there was probably another option under consideration before.

Swedish often places istället late in the sentence, especially after the thing being chosen:

• Vi åt hemma istället. = We ate at home instead.
• Hon tog tåget istället. = She took the train instead.

Its placement here sounds very natural.

Snabbt is an adverb meaning quickly. It modifies the process of becoming agreed.

So:

• Vi blev snabbt överens = We quickly agreed

This word order is normal in Swedish. In a main clause, adverbs often come after the finite verb unless something else causes a different order.

Here the structure is:

• Vi = subject
• blev = finite verb
• snabbt = adverb
• överens = complement

So the sentence flows naturally as Vi blev snabbt överens ...

Yes, överens behaves like an adjective, but it is one of those words that does not change form in the usual way.

So you say:

• Jag är överens
• Vi är överens
• Hon blev överens med dem

There is no separate plural ending here. You do not change it to match vi.

This is something learners just have to get used to: some Swedish adjective-like words are fixed in form.

Yes, absolutely. Komma överens is another very common expression meaning to agree or to come to an agreement.

So these are both possible:

• Vi blev snabbt överens om att ta bussen istället.
• Vi kom snabbt överens om att ta bussen istället.

They are very similar in meaning. In many contexts, both sound natural.

Very roughly:

• bli överens emphasizes the resulting state of agreement
• komma överens is the more standard fixed expression for reach agreement

In everyday Swedish, komma överens is extremely common.

Because för att usually introduces purpose: in order to.

Examples:

• Vi gick till hållplatsen för att ta bussen. = We went to the stop in order to take the bus.

But in your sentence, the phrase is not expressing purpose. It is expressing what they agreed on.

So Swedish uses:

• överens om att ... = agreed to ... / agreed that ...

That is why om att is correct here, not för att.

Usually yes, in this kind of sentence.

But it is useful to notice that Swedish often expresses this idea with a structure that literally feels closer to we became in agreement or we came into agreement.

That is why learners should remember the Swedish pattern as a chunk:

• bli överens om att ...
• komma överens om att ...

If you translate too word-for-word from English agree, you might miss this very common Swedish structure.

Yes, some parts can move, but the original version is very natural.

For example:

• Vi blev snabbt överens om att ta bussen istället.
• Snabbt blev vi överens om att ta bussen istället.
  This is possible, but less neutral and more stylistic.
• Vi blev överens snabbt om att ta bussen istället.
  Possible, but less natural than the original.
• Vi blev snabbt överens om att istället ta bussen.
  Also possible, with slightly different emphasis.

The original sentence is a very standard, idiomatic way to say it.