1st your goal is most likely to generate sales or leads for you or your client. If that is the case what does it matter where the lead came from. What matters is finding where your potential customers are and reaching them.
Bing's market share is at 16.3% vs Google 67%. So Bing has 1 out of every 6 search customers.
So by ignoring Bing you are ignoring potential customers.
But when you pay attention to the backlinks from Bing you are diversifying your linking strategy. They saying goes "you should not put all of your eggs in one basket."