Det ser ud til, at forsinkelsen bliver længere, så jeg har tænkt mig at tage bussen i stedet.

Det ser ud til, at ... is a very common way to say It looks like ... or It seems that ....

So:

Det ser ud til, at forsinkelsen bliver længere
= It looks like the delay is getting longer

It does not always mean something is literally visible with your eyes. Just like English it looks like, Danish uses this expression for a conclusion based on the situation.

You can think of it as:

• Det ser ud til = it seems / it looks like
• at ... = that ...

A very close alternative is Det lader til, at ..., which also means It seems that ....

Here at is the conjunction meaning that.

The expression is built like this:

• Det ser ud til = it seems / it looks
• at ... = introduces the full clause that follows

So Danish is saying:

It seems that the delay is getting longer.

Even though til often means to, here it belongs to the fixed expression ser ud til. Then a new clause begins with at.

So do not read it as one unit meaning to that. It is:

• ser ud til = fixed phrase
• at forsinkelsen bliver længere = the clause being introduced

Forsinkelsen means the delay, while en forsinkelse means a delay.

In this sentence, the speaker is talking about a specific delay that is already known from the context, so Danish uses the definite form:

• en forsinkelse = a delay
• forsinkelsen = the delay

This is very common in Danish: if both speaker and listener know which thing is meant, the noun usually appears in the definite form.

Also notice how Danish usually makes the definite form by adding an ending:

• forsinkelse → forsinkelsen

Yes. Bliver længere literally means becomes longer or is getting longer.

In this context, forsinkelsen bliver længere means the delay is increasing. In natural English, you would usually say:

• the delay is getting longer
• the delay is increasing

So:

• bliver = becomes / gets
• længere = longer

This is a very normal Danish way to describe change:

• Det bliver værre = It’s getting worse
• Dagen bliver længere = The day is getting longer

Så here means so.

It connects the first idea to the result or decision in the second idea:

• Det ser ud til, at forsinkelsen bliver længere = It looks like the delay is getting longer
• så jeg har tænkt mig at tage bussen i stedet = so I intend to take the bus instead

So så introduces the consequence or response.

Be careful: så can also mean then, depending on context, but here it clearly means so.

Jeg har tænkt mig at ... means I intend to ... or I’m planning to ....

So:

jeg har tænkt mig at tage bussen
= I intend to take the bus
= I’m planning to take the bus

This is a very common Danish expression for intention.

Breakdown:

• jeg har tænkt mig = literally something like I have thought myself
• at tage bussen = to take the bus

But you should learn har tænkt mig at as a whole expression, because the literal meaning does not help much.

Compared with other options:

• jeg vil tage bussen = I want to / will take the bus
• jeg skal tage bussen = I’m going to / have to take the bus
• jeg har tænkt mig at tage bussen = I’m intending / planning to take the bus

This version sounds a bit thoughtful and deliberate.

Danish often uses tage (take) with means of transport, just like English does in expressions such as take the bus.

So:

• tage bussen = take the bus
• tage toget = take the train
• tage metroen = take the metro

This is completely normal Danish.

You can also say:

• køre med bussen = go/travel by bus, ride the bus

But tage bussen is very natural when you mean choosing that form of transport.

I stedet means instead.

So:

tage bussen i stedet
= take the bus instead

It usually comes late in the clause, often after the thing being chosen.

Examples:

• Jeg tager toget i stedet. = I’m taking the train instead.
• Vi kan gå i stedet. = We can walk instead.

In your sentence, it contrasts the bus with some other option, probably waiting for something else.

A fuller version can also be:

• i stedet for ... = instead of ...

For example:

• Jeg tager bussen i stedet for toget. = I’m taking the bus instead of the train.

This is normal main-clause word order in Danish.

The basic structure is:

• jeg = subject
• har = finite verb
• tænkt mig = rest of the verbal expression
• at tage bussen = infinitive phrase

So:

jeg har tænkt mig at tage bussen

Danish main clauses usually follow the V2 rule, where the finite verb is in second position. Here the subject comes first, so the verb comes right after it:

• jeg
  • har

If something else were placed first, the subject would move:

• I stedet har jeg tænkt mig at tage bussen.
  = Instead, I intend to take the bus.

So the sentence you have is straightforward main-clause word order.

Because the two at words in this sentence do different jobs.

1. at in Det ser ud til, at ...
   This at is a conjunction meaning that. It introduces a clause.

2. at in har tænkt mig at tage ...
   This at is the infinitive marker, like English to in to take.

So:

• at forsinkelsen bliver længere = that the delay is getting longer
• at tage bussen = to take the bus

There is no at before bliver because bliver is a finite verb in a full clause, not an infinitive.

Yes, in standard Danish spelling, a comma before at is very common when at introduces a subordinate clause, as it does here:

Det ser ud til, at forsinkelsen bliver længere ...

Danish comma rules have varied over time, and you may see some differences depending on style or what comma system is being used, but this comma is completely normal and standard.

For a learner, it is a good idea to get used to seeing commas before subordinate clauses in Danish.

Yes. The original sentence is already natural, but there are simpler alternatives.

For example:

• Det ser ud til, at forsinkelsen bliver længere, så jeg tager bussen i stedet.
  = It looks like the delay is getting longer, so I’ll take the bus instead.

This version removes har tænkt mig at, which makes it a bit more direct.

Another possibility:

• Forsinkelsen ser ud til at blive længere, så jeg tager bussen i stedet.

This is also very natural and slightly more compact.

The original version sounds a little more like a considered decision: I’m planning/intending to take the bus instead.

In careful speech:

• bliver is roughly like BLEE-ver
• længere is roughly like LENG-er-uh

But in real spoken Danish, vowels often become weaker and syllables may be reduced.

A few useful notes:

• bliver is often pronounced more softly than it looks
• længere has the Danish æ sound, which does not match English exactly
• ser ud til may sound quite connected together in fast speech

If you are learning pronunciation, it is best to listen to native audio rather than relying too much on English-style approximations, because Danish spelling and pronunciation often differ quite a lot.