Bilo da slavimo kod kuće ili u restoranu, mojoj baki je svejedno dok smo zajedno.

It means whether ... or ....

So:

• Bilo da slavimo kod kuće ili u restoranu = Whether we celebrate at home or in a restaurant

This is a very common Croatian pattern for presenting two alternatives. In practice, it is best to learn bilo da ... ili ... as a fixed expression.

Historically, yes, bilo is related to biti (to be), but in this construction it does not really function like an ordinary past-tense verb.

In bilo da ... ili ..., learners should treat bilo da as a set conjunction meaning whether. So you do not need to analyze it as a normal verb every time.

Slavimo is the 1st person plural present tense of slaviti (to celebrate).

It means we celebrate.

Croatian often uses the present tense in subordinate clauses even when English might use present or future depending on context. So slavimo can fit naturally even if the celebration is happening now, generally, or in the future.

Because Croatian usually drops subject pronouns when the verb ending already shows the person.

• slavimo already means we celebrate
• smo already means we are

So mi is unnecessary unless you want emphasis or contrast.

For example:

• Mi slavimo kod kuće, a oni u restoranu. = We celebrate at home, and they in a restaurant.

In your sentence, the neutral style is to leave mi out.

Because kod kuće is the normal idiomatic way to say at home.

• kod kuće = at home
• u kući = in the house

So the difference is:

• kod kuće focuses on being at one’s home in general
• u kući focuses more literally on being inside the house/building

Also, kod takes the genitive, which is why you get kuće.

Because u can take different cases depending on meaning:

• u + locative = location, in / at
• u + accusative = motion, into / to

Here the meaning is location:

• u restoranu = in / at the restaurant

If you were talking about movement, you would say:

• Idemo u restoran. = We are going to the restaurant.

Because the phrase je svejedno uses the dative for the person who feels that something does not matter.

So:

• mojoj baki je svejedno = it is all the same to my grandmother
• more natural English: my grandmother doesn’t mind / doesn’t care

Here:

• mojoj = dative singular feminine of moja
• baki = dative singular of baka

This is a very common Croatian pattern:

• Meni je svejedno. = I don’t mind.
• Njemu je svejedno. = He doesn’t care.

Here svejedno means it’s all the same, it doesn’t matter, or someone doesn’t mind.

So mojoj baki je svejedno means that your grandmother does not care which option is chosen.

In this sentence, the options are:

• celebrating kod kuće
• celebrating u restoranu

Because je is a clitic, and Croatian clitics usually go in the second position in the clause.

In this clause, mojoj baki comes first, so je follows it:

• mojoj baki je svejedno

This may feel unusual to an English speaker, but it is normal Croatian word order.

You can also hear slightly different orders depending on emphasis, but the placement of je is not random.

Here dok means as long as.

So:

• dok smo zajedno = as long as we are together

Croatian dok can have different meanings depending on context, including:

• while
• until
• as long as

In this sentence, as long as is the right interpretation.

Smo is the short present-tense form of biti for we are.

Zajedno is an adverb meaning together.

So:

• smo zajedno = we are together

Croatian uses the short form smo in normal, neutral sentences. A full form like jesmo is more emphatic and would not be the usual choice here.

Because Bilo da slavimo kod kuće ili u restoranu is an introductory subordinate clause, and Croatian normally separates it from the main clause with a comma.

So the structure is:

• subordinate clause: Bilo da slavimo kod kuće ili u restoranu
• main clause: mojoj baki je svejedno dok smo zajedno

This comma is standard and natural in written Croatian.