This is going to be pretty similar to Google, exept you are going to use BING.com

Type In "Bing Submit URL" in either Bing Or Google, It Will show up on both.

You want to click the first link. "Submit Your Site To Bing"

Depending on your liking, Bing Uses this to prove you're not a robot where Google likes to use pictures to prove it.

Hit Submit! And your website has also been submitted to Bing!