You're trying to update the record (which to me means "change a value on an existing record and save it back"). So you need to retrieve the object, make a change, and save it.
using (var db = new MyContextDB())
{
var result = db.Books.SingleOrDefault(b => b.BookNumber == bookNumber);
if (result != null)
{
result.SomeValue = "Some new value";
db.SaveChanges();
}
}