The 29-year-old singer-and-actress is said to have "fallen hard and is smitten" with the 42-year-old Smashing Pumpkins singer since they started "officially dating" some months ago - much to the disapproval of her friends.
A source told `E!`: "They think he`s too old for her. No one takes any of her boyfriends seriously anymore because she has had so many. They`re sick of all of them being `The One.` "
The pair were first romantically linked in November when they met at a party in Los Angeles.
A source said: "She has completely fallen for Billy and his easygoing, smart attitude. She says she wants to take things a lot further.
"She had secretly been crushing on him for months and felt there was a connection at the party.
"As the night went on things got more intense and they talked with their faces just inches apart."
In September, Jessica revealed her admiration for Billy.
She wrote on her twitter page: "My friend, BillyCorgan, has a pure and enlightening outlook on faith. Go to his new website!"