I would cling to the idea that as long as you are not transporting a rideable or assembled bicycle that it is not a “bicycle” but, in fact, merely a collection of bicycle parts.
So, depending on exactly how the question was asked I might have been able to answer “no” to Continental in your situation. But, I know I would not have been able to lie about what was in the bag. I would have simply been silent after stating “no.”
David K