Learn Hardcore Dutch: De bus is weg.

Weg here means gone/away: it states that the bus is no longer present. It’s not the noun de weg (the road). You can tell because there is no article before weg, and it follows is. The noun meaning needs an article: de weg.

Examples:

De bus is weg. = The bus is gone.
De weg is smal. = The road is narrow.

What part of speech is weg in this sentence?

It functions as a predicative complement (often treated as an adjective/adverb). It does not inflect:

De bussen zijn weg. (not wege)

Similar words used this way: kwijt (lost), klaar (ready), stuk (broken).

Why is it is and not gaat or heeft?

Because it describes a state. Dutch uses zijn (is) + a predicative to express states.

De bus is weg. = The bus is gone (state/result).
De bus gaat weg. = The bus is going away (action in progress or about to happen).
De bus is vertrokken. = The bus has departed (focus on the departure event). Using heeft here is ungrammatical.

How do I say it more explicitly as “The bus has left/departed”?

Neutral/formal: De bus is vertrokken.
Colloquial/result-focused: De bus is weg.
With “leave” verb: De bus is weggegaan. (fine, but for scheduled transport vertrokken is most idiomatic)

How do I negate it or say “not yet”/“already”?

Not gone: De bus is niet weg.
Not gone yet: De bus is nog niet weg.
Already gone: De bus is al weg.
Has been gone for a while: De bus is allang weg.

Can I say De bus is er niet instead? Does it mean the same?

Not exactly.

De bus is weg implies it was there and has left.
De bus is er niet simply says it isn’t there; it may not have arrived yet. Examples:
At 8:05, after the 8:00 bus left: De bus is weg.
At 7:55, while waiting: De bus is er nog niet.

How do I turn it into a yes–no question?

Invert subject and verb:

Is de bus weg?

With adverbs:

Is de bus al weg? (already)
Is de bus nog niet weg? (not yet)

Why de bus and not het bus? What’s the gender and plural?

Bus (vehicle) is a common-gender noun, so it takes de. Plural: de bussen. Diminutive: het busje.

How do I refer back to de bus with a pronoun?

For common-gender nouns use hij or die:

Hij is weg.
Die is weg. Don’t use het for de bus.

How do I pronounce De bus is weg?

Approximate IPA (standard northern Dutch): [də bʏs ɪs ʋɛx]. Tips:

de: reduced vowel [də].
bus: u is [ʏ], like German ü in müssen.
w: [ʋ], between English v and w.
Final g in weg: a guttural (like Scottish “loch”); in the south often a softer [ɣ].

Can weg be used with other subjects in the same way?

Yes:

Hij is weg. (He is gone.)
Mijn sleutels zijn weg. (My keys are gone/missing.)
De sneeuw is weg. (The snow is gone.)

How do I talk about the past?

State in the past: De bus was al weg.
With a time clause: Toen we aankwamen, was de bus al weg.
Event-focused perfect: De bus is vertrokken. / De bus is net vertrokken.

Does weg inflect or come before a noun?

No. In the sense “gone,” weg is predicative and doesn’t take endings, and it’s not used attributively. Use a participle or a verb instead:

de vertrokken bus (the departed bus)
de weggelopen kat (the cat that ran away, using the separable verb weglopen)