Htela bih da pozovem komšinicu na rođendan.

Because Serbian often leaves out subject pronouns when the verb already shows who the subject is.

In bih and pozovem, the I meaning is already clear, so ja is unnecessary. You could say Ja bih htela da pozovem komšinicu na rođendan, but that usually adds emphasis, such as I would like to invite the neighbor, not someone else.

Htela bih is the normal Serbian way to say I would like or I would want in a polite, tentative way.

It is built from:

• htela = the l-participle of hteti (to want), feminine singular
• bih = the conditional auxiliary

So although htela looks like a past form, the whole expression htela bih does not mean simple past here. Together, it forms the conditional: I would like.

Yes. Htela shows that the speaker is female.

If the speaker were male, it would be:

• Hteo bih da pozovem komšinicu na rođendan.

This gender agreement is very common in Serbian with forms like sam htela / sam hteo, bih htela / bih hteo, and similar patterns.

Bih makes the sentence softer and more polite.

Compare:

• Hoću da pozovem komšinicu na rođendan. = I want to invite the neighbor to the birthday party.
  This is more direct.
• Htela bih da pozovem komšinicu na rođendan. = I would like to invite the neighbor to the birthday party.
  This sounds more polite, tentative, or courteous.

English often uses would like in the same way.

In Serbian, after many verbs and expressions, especially those involving wanting, planning, or being able, it is very common to use da + present tense instead of an infinitive.

So Serbian says:

• Htela bih da pozovem...

rather than something like:

• Htela bih pozvati...

The infinitive does exist in Serbian, but da + present is extremely common and often the most natural choice in everyday speech.

This is mainly about aspect.

• pozvati / pozovem is perfective
• pozivati / pozivam is imperfective

Here, the speaker means a single completed action: to invite someone once. That is why pozovem is used.

Pozivam would suggest an ongoing, repeated, or habitual action, which does not fit as well here.

As for zovem, it can mean I call or I am calling, and depending on context it may mean invite, but pozvati is clearer and more natural when you specifically mean invite someone.

Because it is the direct object of the verb, so it goes into the accusative case.

Base form:

• komšinica = neighbor (female), nominative singular

In this sentence:

• pozovem koga? = whom do I invite?
• answer: komšinicu

So:

• nominative: komšinica
• accusative: komšinicu

This -a → -u change is a very common pattern for feminine nouns in Serbian.

Serbian has no articles, so the noun itself does not tell you whether it means the, a, or sometimes even my in a loose contextual sense.

So komšinicu could mean:

• the neighbor
• a neighbor
• my neighbor

Context decides. In many situations, listeners will understand it as a specific female neighbor known to the speaker.

If you want to be more explicit, you could say:

• moju komšinicu = my neighbor
• jednu komšinicu = a neighbor
• tu komšinicu = that neighbor

Na rođendan means to a birthday / to the birthday party.

After na, Serbian often uses:

• accusative for movement toward a place or event
• locative for being at a place or event

Here, the idea is invitation to an event, so accusative is used:

• na rođendan

The noun rođendan is masculine inanimate, and in the singular its accusative looks the same as the nominative, so the form does not change.

Compare:

• Idem na rođendan. = I’m going to the birthday party.
• Bila sam na rođendanu. = I was at the birthday party.

Notice the second one uses na rođendanu because it is location, not direction.

It is left vague unless context makes it clear.

Na rođendan can simply mean to a birthday party. In real conversation, people often already know whose birthday is being discussed.

If needed, Serbian can specify:

• na moj rođendan = to my birthday party
• na njen rođendan = to her birthday party
• na rođendan mog sina = to my son’s birthday party

Because bih is a clitic, and Serbian clitics usually go in the second position of the clause.

So the natural order is:

• Htela bih da pozovem komšinicu na rođendan.

Not normally:

• Bih htela da pozovem...

This second-position rule is very important in Serbian. Clitics like sam, si, je, smo, ste, su, bih, bi, bih, and object pronouns often follow it.

Yes, Serbian word order is fairly flexible, but the neutral version is the one you have here.

Neutral:

• Htela bih da pozovem komšinicu na rođendan.

You can move things for emphasis, for example:

• Komšinicu bih htela da pozovem na rođendan.
  Emphasis on the neighbor
• Na rođendan bih htela da pozovem komšinicu.
  Emphasis on to the birthday party

Even when the order changes, the clitic bih still tends to stay in second position.

Yes. All of these are possible, but they have slightly different shades of meaning.

• Htela bih = I would like / I’d want to
• Želela bih = I would like / I would wish to, often a bit more formal or deliberate
• Volela bih = very common for I would like, often especially natural in polite speech

So these are all possible:

• Htela bih da pozovem komšinicu na rođendan.
• Želela bih da pozovem komšinicu na rođendan.
• Volela bih da pozovem komšinicu na rođendan.

In everyday conversation, volela bih is often especially common for polite I’d like.

Yes. Komšinica is feminine and means a female neighbor.

The masculine form is:

• komšija = male neighbor

So if the neighbor were male, the sentence would be:

• Htela bih da pozovem komšiju na rođendan.

Notice the accusative:

• komšija → komšiju
• komšinica → komšinicu