When Wickham says "it is believed" that Darcy & Anne De Bourgh will get married, he doesn't indicate who believes this will happen. While still a lad, he may have heard Lady C say it or perhaps his father (Wickham, Sr.) or maybe one of Darcy's parents. Wickham does not say that the two cousins are engaged, nor does he say that Darcy intends to marry his cousin.

We don't know how much Caroline knows about Darcy's family, and we really don't know if Bingley himself knows anybody in Darcy's family (other than Georgiana). So it's possible that any such belief or even rumour of a pre-engagement is completely unknown to Bingley and his sisters.