Jag kunde ha tagit bron som genväg, men jag gick fel väg i stället.

Because kunde ha tagit is the normal way to say could have taken about a past possibility that did not happen.

• kunde = could
• ha tagit = have taken

So the whole phrase expresses an unrealized option in the past:

• Jag kunde ha tagit bron = I could have taken the bridge

This is different from a simple past statement like Jag tog bron = I took the bridge.

Swedish modal verbs usually take the infinitive without att.

Common modal verbs include:

• kunna = can, be able to
• vilja = want
• måste = must
• ska = shall, will, be supposed to
• få = may, be allowed to

So you say:

• Jag kunde ta bron
• Jag kunde ha tagit bron

not:

• Jag kunde att ta bron

Because after ha in this kind of structure, Swedish uses the supine form of the verb.

For ta:

• infinitive: ta
• past tense: tog
• supine: tagit

So:

• ha tagit = have taken

This is the same pattern as:

• har gått = has gone
• hade sett = had seen
• kunde ha gjort = could have done

Bron is the definite singular form of bro.

• en bro = a bridge
• bron = the bridge

So ta bron means take the bridge. The definite form suggests a specific bridge, probably one already known from the situation or context.

Here som means as, so som genväg means as a shortcut.

• genväg = shortcut
• som genväg = as a shortcut

So:

• ta bron som genväg = take the bridge as a shortcut

This use of som is common when something is being used in a certain role or function:

• använda stolen som stege = use the chair as a ladder
• ha köket som kontor = use the kitchen as an office

In Swedish, when som means as and describes a role or function, the noun often appears without an article.

So Swedish prefers:

• som genväg

rather than:

• som en genväg

Both may be understandable in some contexts, but som genväg sounds more natural here.

Literally, it is went wrong way.

More natural English would be:

• went the wrong way
• went the wrong route
• got on the wrong path

This is an idiomatic Swedish expression. Swedish often leaves out the article in expressions like this.

Compare:

• gå fel väg = go the wrong way
• ta fel buss = take the wrong bus
• ringa fel nummer = dial the wrong number

Both can work, but they focus on slightly different things.

• gå fel väg emphasizes the movement: go the wrong way
• ta fel väg emphasizes the choice of route: take the wrong route

In this sentence, gick fel väg sounds very natural because it describes what the speaker actually ended up doing physically.

I stället means instead or instead of that.

So:

• men jag gick fel väg i stället = but I went the wrong way instead

It marks a contrast between the first possibility and what actually happened.

You may also see the spelling istället. Both are used.

That is a very natural position for it in Swedish. Putting i stället at the end gives a clear contrast with the earlier idea.

• Jag gick fel väg i stället = I went the wrong way instead

You can also move it earlier for emphasis, but then the word order changes:

• I stället gick jag fel väg

Because Swedish is a verb-second language, when an adverbial like I stället comes first, the verb usually comes before the subject.

Because men is a coordinating conjunction, like but in English. It does not cause inversion by itself.

So the normal order stays:

• men jag gick fel väg

If something else were placed first in the clause, then you would get inversion:

• I stället gick jag fel väg

So the important point is:

• after men alone: subject + verb
• after a fronted adverbial: verb before subject

Here it expresses possibility in the sense of an available option.

So Jag kunde ha tagit bron is not mainly about physical ability, like I was able to take the bridge. It means more:

• I could have taken the bridge
• That was an option available to me

In other contexts, kunna can mean ability:

• Jag kan simma = I can swim

But here it is about a missed possibility in the past.

It is most naturally understood as a real route:

• there was a bridge
• it could have been used as a shortcut
• instead, the speaker went the wrong way

Grammatically, though, parts of it could be used metaphorically in another context. For example, gå fel väg can sometimes be understood figuratively as go down the wrong path. In this sentence, however, the presence of bron and genväg strongly suggests a literal route.