Ok guys here's a little update.
Billy is absolutely TERRIFIED of Sunni. Like horribly afraid of her. I put them in the bathroom together and Billy was so scared of her that she was climbing all over me, shaking, and even trying to fly into the bathtub to get away from her. Sunni was just preening herself, at least she isn't scared of Billy as well. But I do not know what to do. It'l only been 3 days since we've gotten Sunni and I know it's a long process to introduce birds but at this point I have 0 hope that things are going to work out.