The Bingley-Jane relationship, as a whole, seems to be a subject of subtleconcern in the novel Pride and Prejudice, by Jane Austen.
We first see a concern when Charlotte Lucas notices that neither Jane nor Bingley seem to take a further step in solidifying their courtship, and seem to be reducing themselves to meeting only at parties or balls.
.....though Bingley and Jane meet tolerably often, it is never for many hours together; and as they always see each other in large mixed parties, it is impossible that every moment should be employed in conversing together. Jane should therefore make the mostof every half hour in which she can command his attention. When she is secure of him, there will be leisure for falling in love as much as she chooses.''
Similarly, Mr. Bennet himself makes an ironic comment regarding the natural tendencies of the couple. They both seem quiet, not too excitable, even a bit shy. He mentions their disposition to act just like each other, and their little energy, compared of course to Elizabeth.
Although the marriage seems to be a successful one, the way in which it became possible leaves a couple of questions regarding Bingley's strength of character and initiative with Jane. Yet, in Austen's world there is a solution for everything, so ultimately their marriage found very little obstacles to succeed.