Biraz daha bekle, otobüs yakında gelecek.

Literally, biraz daha means a little more. In this sentence, though, it is best understood as a little longer or a bit more in time:

• Biraz bekle = Wait a little
• Biraz daha bekle = Wait a little longer

So daha adds the idea of more / further.

Bekle is the informal singular imperative form of beklemek (to wait). It is used when telling one person to do something:

• bekle = wait
• gel = come
• otur = sit

So Biraz daha bekle means Wait a little longer.

By contrast:

• bekliyorsun = you are waiting
• bekleyeceksin = you will wait
• bekleyin = wait (plural or polite)

Turkish often leaves out subject pronouns when they are already clear from the verb form or the situation.

In an imperative, the subject is naturally understood as you, so sen is usually omitted:

• Bekle = Wait
• Sen bekle = You wait (more emphatic, often unnecessary)

So the sentence sounds natural without sen.

Here, yakında means soon or in the near future.

So:

• Otobüs yakında gelecek = The bus will come soon

In other contexts, yakında can also relate to the idea of nearby / close by, but in this sentence the time meaning, soon, is the natural one.

Gelecek is the future tense of gelmek (to come) in the third person singular:

• gelmek = to come
• gelecek = he/she/it will come

Since the subject is otobüs (the bus), Turkish uses the third person singular:

• Otobüs gelecek = The bus will come

So yakında gelecek means will come soon.

Yes, gelecek can also mean the future as a noun. But here it is clearly a verb because of the sentence structure:

• Otobüs yakında gelecek = The bus will come soon

After the subject otobüs, you expect a predicate, and gelecek works as the verb. So in this sentence it is not the noun future.

Turkish does not have a definite article like English the.

So otobüs can mean:

• a bus
• the bus

The exact meaning depends on context. In this sentence, it most naturally means the bus, because both speaker and listener probably know which bus is being talked about.

No, Turkish word order is flexible, although some orders sound more neutral than others.

Otobüs yakında gelecek is a very natural order:
subject + time adverb + verb

You could also hear:

• Yakında otobüs gelecek
• Otobüs gelecek yakında (possible, but more marked)

The basic meaning stays the same, but the emphasis may shift slightly. The version in your sentence is neutral and common.

The comma separates two clauses:

• Biraz daha bekle
• otobüs yakında gelecek

It works like English: Wait a little longer, the bus will come soon.

The comma shows a pause between the command and the explanation/result.

You would usually change bekle to bekleyin:

• Biraz daha bekleyin, otobüs yakında gelecek.

That can mean:

• Wait a little longer (to several people)
• Please wait a little longer (polite singular or plural)

You can make it even softer by adding lütfen:

• Lütfen biraz daha bekleyin, otobüs yakında gelecek.

In this sentence, the word is otobüs, spelled with ü, not ö.

A rough pronunciation is:

• o-to-BÜS

The ü is a front rounded vowel. If you know French or German, it is similar to French u or German ü.

A helpful trick for English speakers:

1. Say ee
2. Keep your tongue in that position
3. Round your lips

That gives you something close to Turkish ü.

So otobüs does not sound like English bus at the end; it has a clear ü sound.