Jenna Bush Hager and Barbara Bush Say There Are Ghosts in the White House: 'There's Unfinished Business!' (Exclusive)

Jenna Bush Hager and Barbara Bush were ghosted while living in the White House — literally.

The twin sisters, both 43, whose father George W. Bush was president from 2001-2009, revealed to PEOPLE in this week's cover story that the famous D.C. residence is haunted.

"Well, there are ghosts in the White House," says Barbara, to which Jenna interjects: "Do you want to do a public apology to me? Because you didn't believe me."

"Yes, I'm sorry," says Barbara. "Do you accept my apology?"

"I accept," muses Jenna. "Barbara didn't believe me the first time. I was sleeping in my room — this was in college — and I woke up and heard opera coming out of the fireplace. And I could feel it! I honestly had chills."

Jenna, who co-authored a new children's book I Loved You First with Barbara, says that their rooms at 1600 Pennsylvania Avenue were right next door to each other, so Jenna leapt out of her bed after hearing the music and ran to Barbara's where she "jumped in" with her twin.

"I'm like 'Barbara, Barbara!' I woke her up. 'I heard something. I think there's a ghost.' I got in bed with her, and we went back to sleep. Two days later she came to sleep in mine and she was like, 'There's no ghost.'"

Barbara admits she didn't believe Jenna — at first.

"Two days later I was sleeping in her room. We were dozing off, and then we heard olden times jazz music coming out of the fireplace again. We were so scared. We wanted to get in bed with our parents, but we were 22 and it felt inappropriate," recalls Barbara with a laugh. "And so then we calmed ourselves down and we thought, 'Well, surely that was the cat. Willard [the cat] was playing the olden jazz music on the piano.'"

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The next morning, says Jenna, she had to be up early for an internship. She walked outside her bedroom to the piano and noticed the top was on, covering the keys. Willard the cat couldn't have been responsible.

For more of Jenna and Barbara's exclusive interview, pick up this week's issue of PEOPLE on newsstands Friday.

"There was a man who we love — who I talked to recently — Buddy, who worked at the White House. And [that morning] I said, 'Buddy, you would not believe what happened,'" says Jenna. "And he goes, 'Jenna, you wouldn't believe what I've heard.'"

"There [are] ghosts," concludes Barbara. "There's a lot of people that have lived in the White House, and I think there's some unfinished business with someone that likes music!"