Bilo da pada kiša, bilo da puše vjetar, kuma će doći rano.

It is a set expression meaning whether ... or ... / be it ... or ... / regardless of whether ... or ....

So in this sentence, bilo da pada kiša, bilo da puše vjetar introduces two alternative circumstances, but the result stays the same: kuma će doći rano.

A good way to think of it is:

• bilo da X, bilo da Y = whether X or Y
• It often implies it makes no difference which condition is true

That is a very common question. Here, bilo da functions as a fixed conjunction-like expression. Even though bilo historically comes from biti, in this pattern it does not really feel like ordinary past tense.

So learners should usually treat bilo da as one unit meaning:

• whether
• whether it be
• regardless of whether

In other words, don’t read it as a literal past tense in this sentence.