My reading of Darcy's letter is that Bingley only has to see a pretty girl who is willing to dance and chat to him to imagine himself in love. Jane is just the next one in the line.

I don't think this makes Bingley a 'player' - there is no suggestion that he has ever given any other young lady the impression that he actually wanted to marry her. He is lively and engaging (and handsome and rich ;) ), and is, therefore, popular with young ladies. However, I don't think he has really been in real love before, just had a series of crushes.

The etiquette of the time, that you didn't just jump into bed with someone you had a passing fancy for, meant that he could 'fall in love' in a casual way over and over again without any blame being attached to him. Remember - Jane, too, has 'liked' other people, but there is no indication that any of those attachments were in any way serious.