From Churchill’s My Early Life, I gained an immense advantage over the clever boys. They all went on to learn Latin and Greek and splendid things like that... We were considered such dunces that we could learn only English... Thus I got into my bones the essential structure of the ordinary British sentence-which is a noble thing.
To get something into your bones means to learn something so thoroughly that it becomes second nature to you. See this link for the meaning of "to the bone", and this previous post. The meaning could also be linked to make one's bones, an idiom meaning to take actions to establish achievement, status, or respect.