Simply put.
-Babcia is used when you are speaking of your Grandmother. (ie: My Babcia was born in Poland and moved to IL.) [Sounds like Bop-Cha]
-Babciu is used when speaking to your Grandmother. (ie: Babciu, how are you today.) {Sounds like Bop-Chew]
Americans pronunce BOB like BAB as if there was an A instead of an O .
Not all American's only the ones in Illinois and most of the midwest. I was taught by my Babcia who is originally from Poland and now lives in IL (I was raised and live in California, spent 2 years in Chicago in my 20's) that It sounds like Bop-Cha or Bop-chew if I am speaking to her. Most people in IL make O's sound like A's.
I suppose you could sound it out Bob-cha or bop-cha. Either way it sounds pretty much the same.
It does not sound like Bop-chee = bop-chi