بعد از اینکه به پل رسیدی، در آن چهارراه به راست بپیچ.

A natural breakdown is:

• بعد از اینکه = after / after the point when
• به پل = to the bridge
• رسیدی = you reached / you arrived
• در آن چهارراه = at that intersection / crossroads
• به راست = to the right
• بپیچ = turn

So the structure is basically:

After you reach the bridge, turn right at that intersection.

A more literal gloss would be:

After that you reached the bridge, at that intersection turn to the right.

This is very common in Persian.

In time clauses with words like وقتی or بعد از اینکه, Persian often uses the simple past form to talk about something that will be completed before the next action happens.

So:

• وقتی رسیدی، خبر بده = When you arrive, let me know
• بعد از اینکه به پل رسیدی، ... = After you reach the bridge, ...

Even though رسیدی is grammatically a past form, here it refers to a future event from the speaker’s point of view.

This is one of those places where Persian and English do not match word for word.

Because the verb رسیدن normally takes the preposition به.

So Persian says:

• به خانه رسیدم = I arrived at home
• به ایستگاه رسیدیم = we reached the station
• به پل رسیدی = you reached the bridge

English reach usually does not need to, but Persian رسیدن does need به.

بپیچ is the imperative form of پیچیدن in the sense of to turn.

Here it is:

• بپیچ = turn!
  
  • singular
  • informal

So it is used when speaking to one person in a familiar way.

Other related forms:

• بپیچید = turn!
  
  • formal singular, or plural
• نپیچ = don’t turn!
• نپیچید = don’t turn! (formal/plural)

So if you were giving the same direction politely, you would say:

بعد از اینکه به پل رسیدید، در آن چهارراه به راست بپیچید.

In Persian, direction words often come with به:

• به راست = to the right
• به چپ = to the left
• به بالا = upward / up
• به پایین = downward / down

So به راست بپیچ literally means turn to the right.

This is very similar to English, where we also often say turn to the right, although in everyday English we usually shorten it to turn right.

چهارراه literally means four-way:

• چهار = four
• راه = road / way

In everyday Persian, چهارراه means a crossroads or intersection, especially a four-way one.

So:

• در آن چهارراه = at that intersection / crossroads

If the road situation is different, Persian might also use words like:

• تقاطع = intersection (more formal)
• سه‌راه = three-way junction
• میدان = roundabout / square, depending on context

Yes, سر چهارراه can also work, and many learners hear it often.

The phrase در آن چهارراه literally means in/at that intersection. It is understandable and natural.

But Persian also commonly uses:

• سر چهارراه = at the intersection
• توی آن چهارراه = in that intersection
• اونجا = there, if the context is clear

So these are all possible depending on style and context:

• در آن چهارراه به راست بپیچ
• سر آن چهارراه به راست بپیچ
• سر چهارراه به راست بپیچ

سر چهارراه is often very idiomatic in spoken Persian for at the crossroads/intersection.

In this sentence, بعد از اینکه works as a fixed expression meaning after or after the point when.

You do not need to translate اینکه separately every time. It is part of the connector.

So:

• بعد از اینکه رسیدی = after you arrive / after you’ve arrived

You can think of it as a clause introducer.

There are also shorter or alternative ways to say something similar, for example:

• وقتی به پل رسیدی، ... = when you reach the bridge, ...
• بعد از رسیدن به پل، ... = after reaching the bridge, ...

So بعد از اینکه is one common way to connect the two parts of the sentence.

It is mostly neutral in wording, but the command form is informal singular because of رسیدی and بپیچ.

That means the speaker is talking to:

• one person
• not in a formal/polite way

A polite version would be:

بعد از اینکه به پل رسیدید، در آن چهارراه به راست بپیچید.

In everyday colloquial Persian, you might also hear:

• بعد از اینکه به پل رسیدی، اون چهارراه به راست بپیچ.
• وقتی به پل رسیدی، به راست بپیچ.

Also note:

• آن is more written or careful
• اون is more colloquial

A useful transliteration is:

ba'd az inke be pol residi, dar ân chahâr-râh be râst bepich

A few pronunciation notes:

• بعد is roughly ba'd
  
  • there is a slight break before the d
• پل = pol
• رسیدی = residi
• چهارراه = chahâr-râh
• راست = râst
• بپیچ = bepich

If you say it smoothly, it sounds something like:

ba'd az inke be pol residi, dar ân chahâr-râh be râst bepich

Yes. That is a very common alternative.

Compare:

• بعد از اینکه به پل رسیدی، ... = after you reach the bridge, ...
• وقتی به پل رسیدی، ... = when you reach the bridge, ...

In many everyday situations, these are very close in meaning.

بعد از اینکه can feel a little more explicit about sequence: first reach the bridge, then do the next thing.

وقتی is often a bit simpler and very common in speech.