Billie Eilish has apparently gone public with her latest alleged love interest. The singer shared her first photo with rumored boyfriend Jesse Rutherford to her 106 million Instagram followers on Tuesday. Amid her Halloween-themed slideshow, Eilish added a snapshot of her and The Neighbourhood frontman to her Instagram carousel. In the final image, the “Bad Guy” singer is in a baby costume, while Rutherford is dressed as an elderly man. There’s an 11-year-age gap between the couple, who first had tongues wagging when they were spotted kissing during a dinner date in Los Angeles last month. A w…