Bugün bankta otururken gözlüğümü düşürdüm, ama hemen buldum.

Because bank in Turkish means bench, while banka means bank as a financial institution.

• bank = bench
• banka = bank

So:

• bankta = on/at the bench
• bankada = in/at the bank

This is a very common point of confusion for English speakers.

-ta is the locative case ending, meaning something like in, on, at depending on context.

Here:

• bank = bench
• bankta = on the bench / at the bench

The ending appears as -da / -de / -ta / -te depending on vowel harmony and consonant voicing. Since bank ends in the voiceless consonant k, the form becomes -ta.

Otururken means while sitting or when sitting.

It comes from:

• oturmak = to sit
• oturur = sits / is sitting / usually sits
• otururken = while sitting

The ending -ken means while or when, and it attaches to a verb form to create a time clause.

So:

• otururken = while I was sitting / while sitting

In this sentence, it gives the background action: the dropping happened during the sitting.

Because Turkish often leaves out subject pronouns when they are clear from the verb ending.

For example:

• düşürdüm = I dropped
• buldum = I found

The ending -üm / -dum already tells you the subject is I, so ben is usually unnecessary unless you want emphasis.

Compare:

• Gözlüğümü düşürdüm. = I dropped my glasses.
• Ben gözlüğümü düşürdüm. = I dropped my glasses.
  This sounds more emphatic.

This happens because of a common sound change in Turkish.

The base word is:

• gözlük = glasses / pair of glasses

When a vowel-starting ending is added, the final k often changes to ğ:

• gözlük
  • -üm → gözlüğüm = my glasses
• gözlüğüm
  • -ü → gözlüğümü

So gözlüğümü means my glasses as a definite direct object.

This k → ğ change is very common in Turkish.

Because it contains two different endings:

1. -üm = my
2. -ü = the definite direct object marker

So the structure is:

• gözlük = glasses
• gözlüğüm = my glasses
• gözlüğümü = my glasses as the thing affected by the verb

Since drop is done to a specific thing, Turkish marks that object.

So:

• gözlüğümü düşürdüm = I dropped my glasses

Because düşmek means to fall, but düşürmek means to drop or to cause to fall.

Compare:

• Gözlüğüm düştü. = My glasses fell.
• Gözlüğümü düşürdüm. = I dropped my glasses.

So in this sentence, the speaker accidentally caused the glasses to fall, which is why düşürmek is the correct verb.

In Turkish, gözlük usually means glasses as in a pair of glasses. Even though English uses a plural form, Turkish often uses this singular-looking noun for the whole item.

So:

• gözlük = glasses / a pair of glasses
• gözlüğümü = my glasses

This is normal and does not sound strange in Turkish.

Because Turkish often leaves out objects when they are obvious from context.

Here, after gözlüğümü düşürdüm, it is clear that buldum means I found it or I found my glasses.

You could also say:

• ama hemen onu buldum = but I found it immediately

That is grammatical, but the original version sounds natural because the object is already understood.

Hemen means immediately, right away, or at once.

In this sentence:

• ama hemen buldum = but I found it immediately

Turkish word order is fairly flexible, so hemen can sometimes move depending on emphasis. But before the verb is a very common position.

For example:

• Hemen buldum. = I found it immediately.
• Ama hemen buldum. = But I found it immediately.

Yes. Turkish often puts the main verb near the end of the clause.

This sentence is structured roughly like this:

• Bugün = today
• bankta = on the bench
• otururken = while sitting
• gözlüğümü = my glasses
• düşürdüm = I dropped
• ama = but
• hemen = immediately
• buldum = I found

A very literal English order would be:

• Today, while sitting on the bench, my glasses I-dropped, but immediately I-found.

That sounds unnatural in English, but it is normal in Turkish.

Yes. That whole part is a time-setting expression and can be understood as:

• Today, while I was sitting on the bench
• When I was sitting on the bench today

Turkish often uses these participle-like forms instead of a full clause with I was.

So instead of saying something more explicit like ben bankta oturuyordum, Turkish can naturally use bankta otururken to give the background action.

Yes. The main verbs are in the simple past tense:

• düşürdüm = I dropped
• buldum = I found

The ending -dı / -di / -du / -dü (with vowel harmony and consonant changes) marks this past tense.

So both main actions happened in the past:

1. I dropped my glasses.
2. Then I found them right away.

The otururken part is not a separate past-tense finite verb; it gives the background time relationship: while sitting.