I’m not sure what the aim is really.
I think a random bot is quite a vague idea.
The single worst “bot” is of course the bot that just resigns on move 1 or 2 depending on when it’s first move is. It’s basically incomparable to any real player though, so it may as well be called 
kyu. Similarly one could have a bot that always resigns on move N and they would all be slightly better than each other.
Then one has to think about what the worst bot that actually plays the game is? They shouldn’t resign “early” or maybe at all?
What if there isn’t a worst “random” bot though. A bot playing randomly will have to choose moves according to a distribution, but I wonder could one pick a distribution for example which was bad enough to on average lose more than win, to a bot playing uniformly randomly.
Or pick tiers of distributions which tend to beat each other on average more often. I suppose in the silliest case one could have bots which only play in subsections of the board and then pass when there’s not more legal moves on those points (assume suicide is forbidden and use something like tromp-Taylor rules to score).
I think this is it though, bots playing moves randomly until game is over and bots “really playing the game” are probably very different and might just be incomparable in a real rating system.