She usually 'stumbles out of bed' [=gets out of bed] around 7:00 am.
I 'stumbled across/on/upon' [='found'] this book by chance.
They 'stumbled on/upon' [='discovered'] a bizarre plot.
(..) Yes you do. Dad! Hello Cooper. Professor Brand. Explain to me how you found this facility. Kind of accidently stumbled upon it. We were on a salvage run... You're sitting in the best kept secret in the world. Nobody stumbles in here, nobody stumbles out. Cooper, please, cooperate with these people. (..)2014 Interstellar
(..) a light switch back here. No, dude, you don't... Grab a seat. You two bozos don't even realize it... but you just stumbled onto... the darkest secret in the history of rock. Go on. I actually saw it once. I used to be a guitar tech. (..)2006 Tenacious D in the Pick of Destiny
(..) No, I don't think he likes you at all. No, I don't like you either. - That R unit might have been stolen. - What makes you think that? I stumbled across a recording while I was cleaning him. He says he belongs to someone called Obi-Wan Kenobi. I thought he might have meant old Ben. (..)1977 Star Wars: Episode IV - A New Hope