People like Mr. Bingley because, unlike his friend Mr. Darcy, he is not arrogant and obnoxious. He doesn't act as if he is too good for the local people. In fact, he has a bright, cheerful, and optimistic disposition. He is the kind of person who is easy-going and generally pleased with life. He is delighted with the neighborhood. He thinks the girls are pretty, and he especially likes the lovely Miss Jane Bennet, who likes him in return. The word for him, in Austen's day, was "amiable."
For example, Bingley cheerfully encourages Darcy to dance at the assembly and points out Elizabeth as a possible partner. But while Mr. Bingley, who sees the cup as half full, thinks Elizabeth is pretty, Mr. Darcy says she isn't pretty enough to tempt him. Given a choice, it's not hard to see why Bingley is the more appealing character.