Recently, I needed to carry a small suitcase with my bike. I always have a some bungee cords attached to my bike for when I do grocery shopping. So instead of walking with both suitcase and bike in each hand, I did the following:
You’ll need the suitcase’s wheels to be robust, so I would expect that this only work with quality brands; I went quite fast with mine without a problem. Another issue to be aware of is that the cords should be a bit loose in order for the rigid handle poles not to break; this also helps while turning.