My mom had something like that, they said it was granulomas, a type of scar tissue, they're harmless except for the bleeding and they develop from old trauma to the nose lining.
The ENT doc went in and removed them, she hasn't had a problem since.
("granuloma" is a general medical term for immune-mediated scarring, don't get too freaked out by the more serious versions you'll see on the internet
)