It's true that Darcy thought Bingley was in and out of love, but it's also true that he said in his letter that he recognized that this time was different -- that was why he acted to separate Bingley from Jane.

Also, Darcy isn't perfect, as you say, but he is depicted as a man with an overdeveloped sense of his duty. Unless he's completely lying, he feels some responsibility for what happened to Lydia and he acts to correct the situation that he feels his negligence allowed to develop. (Note: I do think Darcy was exaggerating his feelings of responsibility to some extent in order to explain his involvement, but I don't think he was lying about them -- I think he did feel some sense of responsibility.)

It's hard for me to believe that a man with Darcy's sense of responsibility would just assume that feelings strong enough to lead Bingley to come close to proposing would just go away. I think he would act to find out if Bingley still had feelings, and given Bingley's open nature, I don't think it would be difficult. In fact, I would think if Darcy were around Bingley, he would be able to discern Bingley's feelings even if he weren't actively trying to. Bingley is a heart-on-his-sleeve kind of guy.