I think you make a good point Silvia A in that Mr. Bennet’s wife and daughters could not get “any satisfactory description” (3) of Bingley from him rather than no description at all. However, I don’t think Mr. Bennet’s description of Bingley was very like Sir John’s description of Willoughby as I suspect they were unsatisfactory for different reasons. Sir John from S&S, Ch. 9:

“As good a kind of fellow as ever lived, I assure you. A very decent shot, and there is not a bolder rider in England.”

“is a pleasant, good humoured fellow, and has got the nicest little black bitch of a pointer I ever saw”

“is as good a sort of fellow… as ever lived… …at a little hop at the Park, he danced from eight o'clock till four, without once sitting down”

Only his last (above) gives Marianne any satisfaction:

"Did he indeed?" cried Marianne, with sparkling eyes, "and with elegance, with spirit?"

"Yes; and he was up again at eight to ride to covert."

"That is what I like; that is what a young man ought to be. Whatever be his pursuits, his eagerness in them should know no moderation, and leave him no sense of fatigue."

Marianne asked about Willoughby’s “manners on more intimate acquaintance… his pursuits, his talents and genius” and Sir John would have been quite happy to oblige her if he understood what she wanted. Sir John is not particularly observant of attributes outside of his narrow interests of hunting and partying so he is incapable of satisfying Marianne’s curiosity as to “the shades of his [Willoughby’s] mind” and so gave an unsatisfactory description. The Bennet ladies know Bingley is a single man of good fortune; what they want to know is what sort of a man he is. Had Mr. Bennet described as much of Bingley and his activities as Sir John did of Willoughby then I think they would have been happy indeed. However Mr. Bennet is not so accommodating as Sir John.

I think Mr. Bennet’s description of Bingley was unsatisfactory because he did not give the basic facts rather he was so noncommittal it conveyed no idea of the actual man. It seems to me that at the very least Mr. Bennet, like Sir William, must have seen that Bingley was “quite young, wonderfully handsome, extremely agreeable” (3) yet he did not let on these very obvious and basic facts to his family for they only found them out from Lady Lucas. I think Mr. Bennet answered their questions in unsatisfying generalities something like Jane Fairfax answered a frustrated Emma’s questions about Mr. Dixon and Mr. Churchill:

She seemed bent on giving no real insight into Mr. Dixon's character, or her own value for his company, or opinion of the suitableness of the match. It was all general approbation and smoothness; nothing delineated or distinguished. …The like reserve prevailed on other topics. She and Mr. Frank Churchill had been at Weymouth at the same time. It was known that they were a little acquainted; but not a syllable of real information could Emma procure as to what he truly was. "Was he handsome?" -- "She believed he was reckoned a very fine young man." "Was he agreeable?" -- "He was generally thought so." "Did he appear a sensible young man; a young man of information?" -- "At a watering-place, or in a common London acquaintance, it was difficult to decide on such points. Manners were all that could be safely judged of, under a much longer knowledge than they had yet had of Mr. Churchill. She believed every body found his manners pleasing." Emma could not forgive her. (E, Ch. 20)