Does the cooper have another fluid, like Citroens eolys fluid?
I've yet to find a definative answer about this, but from reading loads about it, I have reached the tentative conclusion, that DPF that regenerate using and additive like eolys, have less problems overall, and are more bio friendly, than ones that generate without.
Even running Dino, DPF are problematic, although it seems that they mostly fail due to an existing problem elewhere, or from the vehicle being driven round like grandma going to church on a sunday morning.
But basically, having no first hand experience of them, I really don't know.
What happens if it won't work on Bio? As far as I know it doesn't do any damage to the engine. The worst it can do is block the exhaust, and you'll know if that starts happening. So may as well leave it in there, and get it removed if or when you have to.