Learn Hardcore Serbian: Rekla sam zbogom prijateljici.

In standard Serbian, the auxiliary sam is a clitic. Clitics usually go in the second position of the sentence or clause, not at the very beginning.

So:

Rekla sam zbogom prijateljici. = natural
Ja sam rekla zbogom prijateljici. = also natural, because sam is now in second position after ja
Sam rekla... = not standard

This is a very common pattern in Serbian past tense.

What does rekla mean, and why does it end in -la?

Rekla is the past active participle of the verb reći (to say).

The ending shows the gender and number of the speaker:

rekao = a male speaker said
rekla = a female speaker said
rekli = plural, or mixed/male group said
re kle = feminine plural said

So Rekla sam... tells you the speaker is female.

What is sam doing in the sentence?