eki made isoide ita node, kesa ha basu de ha naku takusii ni norimasita.

駅まで means to the station or more literally as far as the station.

• 駅 = station
• まで = up to / until / as far as

With places, まで often marks the endpoint of movement. In this sentence, it shows the destination of the hurrying: I was hurrying to the station.

急いでいた is the -te iru form in the past, so it means something like:

• was hurrying
• was in a hurry

Breakdown:

• 急ぐ = to hurry
• 急いでいる = is hurrying / is in a hurry
• 急いでいた = was hurrying / was in a hurry

Using 急いだ would sound more like hurried as a completed action.
Here, the speaker wants to describe the situation that was ongoing at the time: because I was in a hurry...

ので means because or since.

In this sentence:

• 急いでいたので = because I was in a hurry

Compared with から, ので often sounds:

• a bit softer
• more explanatory
• a little less direct

So:

• 急いでいたから、... = because I was in a hurry...
• 急いでいたので、... = because I was in a hurry...

Both are correct, but ので often feels slightly more natural in calm explanation.

This is completely normal in Japanese.

In subordinate clauses, Japanese usually uses the plain form, even in otherwise polite sentences.

So:

• 急いでいたので = plain form inside the reason clause
• 乗りました = polite form in the main sentence

This kind of mixing is standard and natural. It is not considered inconsistent.

今朝は sets this morning as the topic or frame for the statement.

• 今朝 = this morning
• 今朝は = as for this morning / this morning

The は can give a slight sense of contrast, like:

• This morning, at least, I took a taxi
• As for this morning, it was a taxi, not a bus

Even when there is no strong contrast, using は after time expressions is very common to set the scene.

ではなく means not... but... or instead of...

Here:

• バスではなく = not by bus / instead of the bus

It is built from:

• で = by / via / using
• は = contrast marker
• なく = negative connective form of ない

So the structure is:

• バスではなく タクシーに乗りました
• I took a taxi, not a bus
• I went by taxi instead of by bus

This is a very common contrast pattern.

They are doing different jobs.

In バスではなく

Here, で is tied to the idea of means/method: by bus.

In タクシーに乗りました

The verb 乗る takes the thing you ride with に:

• バスに乗る = ride a bus
• タクシーに乗る = ride a taxi
• 電車に乗る = ride a train

So the sentence shifts a little in structure:

• not by bus
• rode/took a taxi

That is why the particles are different.

Because in Japanese, when talking about transportation, it is very natural to say ride/take the vehicle.

So:

• タクシーに乗りました = I took a taxi
• バスに乗りました = I took the bus

English often says go by taxi or take a taxi.
Japanese very often prefers the equivalent of ride/take with 乗る.

You could use a verb like 行く in other sentence patterns, but タクシーに乗る is the most natural choice here.

It can naturally mean both.

With 急ぐ, Japanese often does not sharply separate:

• to hurry
• to be in a hurry

So 駅まで急いでいたので can be understood as:

• because I was hurrying to the station
• because I was in a hurry to get to the station

Both are good interpretations.

Japanese often leaves out the subject when it is obvious from context.

So the sentence does not explicitly say I, but in a natural context it is understood as something like:

• I took a taxi this morning because I was in a hurry to get to the station

This omission is extremely common in Japanese.

The structure is:

Reason clause + main clause

• 駅まで急いでいたので、
  • because I was hurrying to the station
• 今朝はバスではなくタクシーに乗りました。
  • this morning, I took a taxi instead of the bus

Japanese often puts the reason first and the main result after it.

Yes. A more casual version could be:

• バスじゃなくてタクシーに乗りました

That would also mean I took a taxi, not a bus.

The differences are mainly in style:

• ではなく = more formal / written / careful
• じゃなくて = more casual / conversational

In your sentence, ではなく matches the polite ending 乗りました nicely.