Bingley probably said good-bye to Jane at the ball:

Mr. Bingley and Jane were standing together, a little detached from the rest, and talked only to each other...

When at length they arose to take leave, Mrs. Bennet was most pressingly civil in her hope of seeing the whole family soon at Longbourn, and addressed herself particularly to Mr. Bingley, to assure him how happy he would make them by eating a family dinner with them at any time, without the ceremony of a formal invitation. Bingley was all grateful pleasure, and he readily engaged for taking the earliest opportunity of waiting on her after his return from London, whither he was obliged to go the next day for a short time.

Taking leave personally with a farewell visit the next day would have been lovely but he did see her the night before and he probably left early. Writing Jane a letter would have been inappropriate. (:D)