I agree with you, I don't think Bingley was honour-bound to propose to Jane, at least not by his public actions. (And I don't think he made any promises in private either.) I would argue that the fact also that the Meryton public seemed to agree Jane had the right to be disappointed, but did not seem to think she was downright jilted, adds to that argument.
Moreover, I think it's good to remember that however naive Bingley may have been in believing Darcy and his sister, he *did* honestly believe Jane did not care for him. It was a wrong assumption, but he operated under it and chose not to return in order to preserve himself and possibly also to preserve Jane from being pushed into marrying him.
Yes, Bingley might have behaved with more grace and taken leave of the neighbourhood in person, but, eh, the man had a broken heart (however easy he might form attachments) and I'm willing to cut him some slack.
And as for Mr Bennet having the duty to take action - it may be just my modern sensibilities, but I couldn't see myself marrying anyone my father had dragged home and forced to marry me just for propriety's sake, if I thought him unwilling.
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