Hmm, our potty lives beside the toilet, and I've never had issues with dribbles (or at least never noticed

)
But if you're talking about the actual
cleaning (ie.disinfecting) part then I had a lightbulb moment the other day about this... I had an extra peri-bottle hanging around and I filled it with a mix of water & pine-sol. Now when he goes potty, I add water to it from the sink, dump & then rinse with the peri bottle solution. If necessary, I wipe with TP. You could also use tea tree oil for the disinfecting purpose (instead of the pine-sol), I just don't care for the smell of TTO.