मैं देर से आने से बच गई।

It means coming late or arriving late.

• देर से = late
• आने = coming / to come in a form used before a postposition

So देर से आने is the idea of arriving late.

Because आना changes to आने when it comes before a postposition like से.

This is often called the oblique infinitive form.

Compare:

• आना = to come
• आने से = from coming / by coming

The same pattern happens with many verbs:

• करना → करने से
• जाना → जाने से
• बोलना → बोलने से

They are doing two different jobs.

1. In देर से, से is part of the expression meaning late or with delay.
2. After आने, से marks the thing being avoided, because बचना / बच जाना often works with से.

So:

• देर से = late
• आने से बच गई = avoided coming / escaped from coming

Together: I avoided arriving late.

Here बच गई means managed to avoid or escaped.

It does not have to mean a dramatic physical rescue. In everyday Hindi, बच जाना is often used for avoiding an unwanted situation.

So in this sentence, the sense is:

• I managed not to arrive late
• I avoided being late

It suggests that being late was possible, but it did not happen.

Because the speaker is understood to be female.

In this sentence, the verb agrees with the subject:

• female speaker: मैं ... बच गई
• male speaker: मैं ... बच गया

So गई tells you that the speaker is feminine singular.

Because बचना / बच जाना is an intransitive verb here.

In Hindi, ने is often used with transitive verbs in the perfective, but not usually with intransitive verbs like this one.

So:

• मैं देर से आने से बच गई। = correct
• मैंने देर से आने से बच गई। = not correct here

Not exactly.

मैं देर से आने से बच गई। has an extra nuance: it suggests that the speaker almost could have been late, but successfully avoided that outcome.

So:

• I was not late = simple fact
• I avoided arriving late = there was a risk, but I escaped it

That makes this sentence a little more expressive than a plain statement of punctuality.

In a sentence like this, it is best understood as the very common compound बच जाना.

That compound often means:

• to escape
• to be spared
• to manage to avoid something

Using गया / गई gives a natural sense of a completed result: the speaker successfully avoided the problem.

So बच गई sounds very natural here.

Yes, that is also possible.

There is a slight difference in focus:

• देर से आने = arriving late / coming late
• देर होने = being late

In many everyday situations, both can work. The given sentence focuses more specifically on the act of arriving late.

Hindi word order is somewhat flexible, though the version you have is the most neutral and natural.

Common order:

• मैं देर से आने से बच गई।

You could also say:

• देर से आने से मैं बच गई।

That might put a little more emphasis on avoiding being late.

The main thing is that the verb usually stays near the end.

Yes, in the right context that is a very good way to understand it.

Because बच गई often carries the idea of escaping an undesirable outcome, the sentence can sound a bit like:

• I just managed not to be late
• I narrowly escaped arriving late

Whether it sounds strong or mild depends on context, but that nuance is definitely there.