Az alkalmi ruha bő.

Hungarian has two forms of the definite article:

• a before a consonant sound
• az before a vowel sound

Since alkalmi starts with a vowel, the correct article is az.

• az alkalmi ruha
• but a ruha

This is similar to English a/an.

In Hungarian, the verb to be is often left out in the present tense, third person.

So instead of saying something like The occasion dress is loose, Hungarian simply says:

• Az alkalmi ruha bő.

This is completely normal.

Compare:

• A ruha szép. = The dress is beautiful.
• A fiú magas. = The boy is tall.

But in other persons, the verb appears:

• Én magas vagyok. = I am tall.
• Te magas vagy. = You are tall.

Alkalmi is an adjective modifying ruha.

So the structure is:

• az = the
• alkalmi = occasion / formal / dressy
• ruha = dress / garment
• bő = loose, roomy

In alkalmi ruha, the adjective comes before the noun, just like in English:

• alkalmi ruha
• szép ruha = beautiful dress
• piros ruha = red dress

Yes, very much. Alkalmi ruha is a common combination and is often understood as a single idea, something like:

• occasion dress
• formal dress
• dressy outfit

So even though it is grammatically just adjective + noun, learners will often meet it as a set phrase.

That is the normal position for a predicate adjective in a simple neutral sentence.

Structure:

• Az alkalmi ruha = the subject
• bő = the description/predicate

So Hungarian is saying:

• The formal dress — loose.

with the present-tense is understood.

This word order is neutral and natural. If you changed the order, you would usually add emphasis or contrast:

• Bő az alkalmi ruha. = The formal dress is loose.
  (with extra emphasis on bő)

Here, no special agreement is visible because ruha is singular.

Important points:

• Hungarian adjectives do not agree for gender, because Hungarian has no grammatical gender.
• In predicate position, adjectives can show plural when the subject is plural.

So:

• A ruha bő. = The dress is loose.
• A ruhák bők. = The dresses are loose.

So in your sentence, bő is singular because ruha is singular.

It is in the nominative case, because it is the subject of the sentence.

Base form:

• ruha = dress / garment

In this sentence:

• Az alkalmi ruha bő.
• The formal dress is loose.

No extra case ending is needed.

Bő is pronounced with a long ő, which is a sound English does not really have.

A rough guide:

• b = like English b
• ő = a long front rounded vowel

It is somewhat like saying a long ö sound with rounded lips.

Also, the accent mark here matters:

• ö = short
• ő = long

So bő has a long vowel.

Yes. Like many adjectives, bő can have different meanings depending on context. Common meanings include:

• loose (clothing)
• roomy
• wide
• ample
• abundant

In this sentence, because it describes ruha, the most natural meaning is:

• loose
• roomy

So the clothing context tells you how to understand it.

Yes, if you just mean The dress is loose.

The difference is that az alkalmi ruha is more specific:

• A ruha bő. = The dress is loose.
• Az alkalmi ruha bő. = The formal/occasion dress is loose.

Also notice the article changes:

• a ruha
• az alkalmi ruha

because ruha starts with a consonant sound, but alkalmi starts with a vowel sound.

A few useful things:

1. No grammatical gender
   Adjectives do not change for masculine/feminine/neuter, because Hungarian does not have those categories.

2. Attributive adjectives come before the noun

   • alkalmi ruha
   • szép ruha

3. Predicate adjectives often appear without a present-tense form of to be

   • A ruha bő.
   • A ruha szép.

So this short sentence is actually a very good example of several basic Hungarian patterns at once.