This is an inverse sentence.
Subject:
- Tanışmamız (Our meeting, our becoming acquainted )
- Tanışmak (to meet, to become acquainted)
-Tanış (root of the verb) + {ma}/me (suffix which makes noun form from verb form, in English it is made by adding -ing to verb such as "to go" --> "going") + {mız} / miz / muz / müz (our, possesion) = Our meeting, our becoming acquainted
Bi = Bir (a,an,one) (It is a street accent)
Tesadüf = Coincidence
-dı/di/du/dü = past tense suffix and after "f,s,t,k,ç,ş,h,p" letters "d" will be "t"
Tesadüftü = It was coincidence
Bi tesadüftü tanışmamız = Our meeting/becoming acquainted was a coincidence.