Bianca sounds just like my Puddles. She is NOT a social cat as she is very timid, doesn't matter how the intro's are done, she hates other cats.
Have you tried giving Bianca her own space? How about bringing her into your bedroom at night, just you and her along with a litter box, food and water so she can relax? We do that for Puddles to keep her and Sweet Pea separate (not going to go into all the history), and it has made a world of difference in Puddles's life. We also keep the cats separated while we are out too. It has made a stressful situation much better on Puddles. I also make sure I make the time to have just "Puddles and me" time, no other cats around, and she just loves it. Is there is something special that Bianca loves to do with you, whether it be brushing, playing with a string, or being carried around the apt. that the two of you can do?
IMHO, it is truly unfair to give up an original cat, to accommodate new comers.
Cat maid to:
Jasper, male Ragdoll ?? (approx 10 yrs)
Rose semi feral, a cpietra rescue, female tabby (approx 7 yrs)
Sweet Pea RIP (2004?-2014)
Puddles RIP (1996-2014)
Snowball RIP (1991-2005)
In a cat's eye, all things belong to cats.-English Proverb
“While we are free to choose our actions, we are not free to choose the consequences of our actions.” Stephen R. Covey