I have not read most of the asteroid wars arc.
How big depends on what they're mining. I'd say a decent 'general purpose' asteroid would be in the 1km+ diameter range but I think that would throw off your scaling pretty bad. There are some mostly-metal asteroids which would be extremely profitable to mine even at your size though as they contain lots of valuable metals and rare-earths.
At the current size it almost makes sense to put a metal band around the asteroid to hold your base in place rather than trying to anchor it. The anchors would have to be quite large and numerous and would depend a lot on unstable geology that's going to shift around as you extract more resources. But an adjustable band around the asteroid (like a belt for your pants) would be secure and adjustable with not much more material going into its construction.
It might look silly but modern problems require modern solutions.