Βάζω το μπουκαλάκι στην τσάντα μου πριν φύγω.

Because Greek often drops subject pronouns when they are not needed.

The verb βάζω already tells you the subject is I:

• βάζω = I put / I am putting

So Εγώ βάζω... is possible, but it would usually add emphasis, like:

• Εγώ βάζω το μπουκαλάκι... = I’m the one putting the bottle in the bag

In a neutral sentence, leaving out εγώ is completely normal.

Βάζω basically means put, place, or sometimes set.

In this sentence, the present tense can be used in a few natural ways:

• as a habitual action: I put the little bottle in my bag before I leave
• as a simple present describing a routine
• sometimes even as a near-future / vivid present, depending on context

Greek uses the present tense quite naturally for things that are part of a routine or sequence.

Μπουκαλάκι is the diminutive form of μπουκάλι.

• μπουκάλι = bottle
• μπουκαλάκι = little bottle / small bottle

The ending -άκι often makes a noun smaller, cuter, or more informal. Sometimes it really means small; other times it just sounds more natural in everyday speech.

So here, το μπουκαλάκι suggests a small bottle, such as a water bottle, medicine bottle, or travel-size container.

Because μπουκαλάκι is a neuter singular noun, and its nominative/accusative singular article is το.

So:

• το μπουκαλάκι = the little bottle

In this sentence, το μπουκαλάκι is the direct object of βάζω, and for neuter nouns, the nominative and accusative article is the same: το.

Στην is the contracted form of:

• σε + την = στην

So:

• στην τσάντα = in the bag / into the bag

With βάζω, this phrase shows where the object is being placed.

A useful point:

• σε is the preposition meaning in, into, at, to
• with the definite article, it often contracts:
  • σε τον → στον
  • σε τη(ν) → στη(ν)
  • σε το → στο

So στην τσάντα is just the normal contracted form.

It is in the accusative case.

After the preposition σε, Modern Greek normally uses the accusative:

• στην τσάντα
• στο σπίτι
• στον φίλο μου

So even though English says in the bag, Greek uses σε + accusative for this kind of location/direction phrase.

That is the normal Greek pattern for possessives with these weak pronoun forms.

Greek usually says:

• η τσάντα μου = my bag
• ο φίλος μου = my friend
• το σπίτι μου = my house

So μου comes after the noun, not before it as in English.

In your sentence, the article is already built into στην, so:

• στην τσάντα μου = in my bag

You do not need an extra article before μου. The structure is already complete.

Because after πριν when talking about a specific event that has not happened yet, Greek normally uses the subjunctive-type form with the aorist stem:

• πριν φύγω = before I leave

Here the meaning is before I leave on that occasion, not before I am leaving.

Φεύγω is the present/imperfective form and describes the action as ongoing or repeated.
Φύγω is used here because the sentence refers to the action of leaving as a single whole event.

Φύγω is the aorist subjunctive form of φεύγω.

Very roughly:

• φεύγω = I leave / I am leaving
• να φύγω = that I leave / for me to leave / I should leave
• πριν φύγω = before I leave

Even though there is no να here, the form φύγω is still the one associated with the subjunctive / perfective system.

Why this form? Because Greek often uses the perfective (aorist) subjunctive form after words like πριν when talking about a single completed event in the future or relative future.

Because πριν does not require να in this structure.

Greek says:

• πριν φύγω = before I leave
• πριν πάμε = before we go
• πριν έρθει = before he/she comes

So this is just the normal pattern:

• πριν + subjunctive-type form

English learners sometimes expect να because they learn many other patterns with it, but after πριν, it is usually omitted in standard Modern Greek.

It can mean either, depending on context.

Most naturally, it can mean:

• a habit/routine: I put the little bottle in my bag before I leave
• a specific present/future situation: I’m putting the little bottle in my bag before I leave

Greek present tense is flexible in this way, just like English simple present can sometimes describe routines and sometimes planned or immediate actions.

Context tells you which meaning is intended.

Yes, Greek word order is fairly flexible, though the original version is very natural:

• Βάζω το μπουκαλάκι στην τσάντα μου πριν φύγω.

You could also hear variations like:

• Πριν φύγω, βάζω το μπουκαλάκι στην τσάντα μου.

This puts more focus on before I leave.

But the original order is a very normal neutral sentence:

1. verb
2. object
3. place phrase
4. time clause

So it sounds natural and straightforward.