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What does "Bi" stand for? is it like bir?

evet

bi = bir

when do I know when I have to say Bi and when I have to say Bir? Or does it not matter?

Personally, I have never noticed this when listening to anyone. You should be able to say it either way. Just realize that ´Bi´ is like a conversational prononciation of Bir.

Here is a good explanation I found (http://ielanguages.com/turkish.html):

Most of the time, the last consonant of bir is not pronounced in daily life.

Bi hafta sonra geliyorum. I’m coming in a week.
Bi saat önce buradaydı. He was here an hour ago.

i don´t think there is difference. 

Merhaba, ben türküm. Size yardımcı olmak istedim. Öncelikle,  "bir = 1" demek.  "Bir" ve "bi" arasındaki fark konuşma diliyle ilgili :

Konuşma dilinde : Bi kitap aldım.

Yazma dilinde : Bir kitap aldım.

Şeklinde kullanılır.

There is no difference between bi and bir, but when you talk someone you say :

Bi kitap aldım.

When you write you say

Bir kitap aldım.

(Sorry for bad english)

As a foreigner, always use ´bir´. They will have a hard time trying to understand you WITHOUT you trying to copy their linguistical shortcuts )