Thank you Kathryn Ann! I see what you are saying but did Lizzy dismiss Caroline and Bingley out of hand? Lizzy makes some argument against each. For Caroline:

"His guilt and his descent appear by your account to be the same," said Elizabeth angrily; "for I have heard you accuse him of nothing worse than of being the son of Mr. Darcy's steward, and of that, I can assure you, he informed me himself." (Ch. 18)

Caroline has no facts to offer admitting she does not “know the particulars” of the Wickham situation—she may not even know it is about a living. She has long been Darcy’s faithful assistant and defender since Netherfield so unsurprisingly says Darcy is not to blame sighting as evidence that “he cannot bear to hear George Wickham mentioned” which might be only the result of a guilty conscious. Caroline’s eager exposure of Wickham’s father as the former steward of Pemberley and her assertion “His coming into the country at all is a most insolent thing” do show her prejudice against Wickham for his social status. Lizzy’s response to Bingley:

"I have not a doubt of Mr. Bingley's sincerity," said Elizabeth warmly; "but you must excuse my not being convinced by assurances only. Mr. Bingley's defense of his friend was a very able one, I dare say; but since he is unacquainted with several parts of the story, and has learnt the rest from that friend himself, I shall venture still to think of both gentlemen as I did before." (Ch. 18)

Lizzy does believe she has the whole story from Wickham. She does not just suppose Bingley “is unacquainted with several parts of the story” she knows he is because Jane admits that he does not know the whole story and he does not remember the circumstances. I think those are rather big parts of the story. Bingley has no facts to offer. His belief the living was left to Wickham conditionally is merely his belief and unfortunately unsupported by his own memory. Bingley is a good character witness for Darcy which Lizzy admits but that is all. His partiality for Darcy and never having done more than touch his hat to Wickham (if that) makes his testimony about each suspect for partiality for his friend.