Thing
It depends how big and how active the CB Is as to how close you will get
You only have to listen to ATC over London to realise what a headache CBs are to ATC when aurcraft are all not being where ATC want them to be asking for 20 degrees left or right and being asked when they can turn back to XYZ?
20 miles ?? Rarely unless it was a very large solid cell
You will avoid even towering cumulus as you don't want PAX jumping off their seats and as SND said there is icing to consider
But CBs and icing whether in CBS or not are probably the two most weather related items to avoid
But how close ? It's a judgement thing last summer there was a huge cell over France trying to keep as close to a desired track and getting closer to the cell meant turbulence so you would naturally give such a cell a wider birth the turbulence itself warning you that you were getting too close to an angry Bull
)
Other cells and you may pass very close in smooth air or cut corners by chopping through a benign edge.
In an ideal world all CBs would be 40 miles apart so you could pass 20 miles between them )) but sadly the real world is rarely like that ((
If your flying for fun and you open the curtains and the weather looks **** close them and stay in bed always fly in your limits and the aircrafts limits
Aircraft limits ? A piston single at 10k at probably the worst icing level minimum performance and little or no de icing anti ice capability ? Stay at home or avoid like mad ))
Pace