Here's a few pairings. Bianca/Thalia/Annabeth, Bianca/Percy/Nico, Bianca/Silena, Bianca/Thalia/Zoe, Bianca/Jason. Thoughts?
Bianca/Thalia/Annabeth (Thaliancabeth) : Ohhhhh that's nice. If Annabeth had become a huntress this three would spend time together as the "new recruits" : Thalia and Annabeth could teach Bianca how to use her powers, they'd do archery contests, games strategy planning (and surprisingly, Bianca is really good at it)... And maybe, I like to imagine, that with Bianca, Annabeth and Thalia could finally reform their little family. Yes there'd still be the other hunters, Annabeth's siblings, Jason (later on) and of course Nico, but they'd have a lovely particular bond, one that could certainly make them leave the hunt one day, to be together like they want to be.
Bianca/Percy/Nico (Biancyco, Percica) : An AU where Percy, after many years of hesitation would finally say "screw it ! I love both of the Hades' children, I'll be with both of the Hades' children !" It would be an euphemism to say that Hades isn't very happy about it. But he wouldn't be able to do anything against it. That's a cool ship, but I'm not a big fan, but the Hades' salt potential is HIGH and FUN.
Bianca/Silena (Silianca, Silenca) : That's nice, really nice. If Bianca had survived and lived in Camp Half-blood they could have become friends, grow closer through the war. Bianca would need someone to help her and her brother with their powers, and Silena seems like the best candidate to motivate her : she clearly is one of the nicest and sweetest campers, she's not her cabin counselor for nothing. Maybe Silena and Charles would still be a thing and Bianca would be the one here to support Silena with Clarisse after his death (and now that I think about it, Bianca/Silena/Clarisse sounds really great too). And I like to imagine Clarisse and Nico helping them to accept and confess their feelings.
Bianca/Thalia/Zoe (Biancalioe, Thaliancoe) : I can't remember where but I'm sure I've already told how cool this ship is : the different combination of hunters are all great, this one is one of the best. Don't have a lot more to say, they would be powerfully cool and lovely.
Bianca/Jason (Biancason, Jasanca) : Told it here, that's awesome and it inspires me a lot for AU.
Great ships here anon, my favorites are Bianca/Jason and Bianca/Silena. Shipping Bianca is really fun, cause she has just enough development to still be pretty easily written by others without risking to be too OOC. And her personality is a perfect mix between sweetness and flaws, I like her and her ships are some of the cutest I have.