What does it mean?

I used to just bug him solid when I was up there because when I was little I was too young to go by myself and I couldn’t saddle the horses up myself

What does ‘bug him solid’ mean?

Well, I don’t know if I am qualified to answer this, as we do not use this phrase in the United States. It must be a Canadian phrase. However, we still “bug” our siblings, meaning we bother them or irritate them. I think adding the word “solid” means that Jill did a very thorough job of bothering her brother!

I used to pester or bother my dad constantly, or all the time, until he’d take me horseback riding.