Otis Cedar

You could use the HDX Tough storage bin, the largest is 55 gal and costs less than US $20 when on sale from Home Depot. They are much stronger than Rubbermaid. With careful feeding you won't need drainage at the bottom. Just drill holes in the lid for air.

Firstly, vermicompost generated from dog manure is not safe to use on edible plants due to possible pathogens. It's OK to use it on ornamental plants.
Secondly, please do not assume that worm compost contain worm cocoons. If any, then possibly just a few. If the vermicompost is processed long enough that all material has been composted and cured that is.
Unless you find a worm farmer who is in a hurry to sell his "black gold", then you might find cocoons and babies and even a few worms that haven't moved along. Since you won't know how many worms you'll start with, you might be waiting for a very long time until the dog pile get processed.
So, adding worm castings to your dog manure pile might not work. Sorry.

Hi Dan, you should probably stop adding Oak leaves to your worm bin as they are highly acidic or so they say.
Larry, the worms you catch from the lawn that come up at night are Night Crawlers and they won't be happu in a worm bin. They are burrowing worms and composting worms are surface dwellers.
Richard might be all confused by now.
If egg shells are fine enough (i.e. powdered), worms will gulp the particals with the food. If not, egg shell particles are still good for the worm bin for neutralizing acidic condition. There's no such thing as too much egg shells since it will just sit their ass egg shells if there's no acid to bind. It will not change the bedding to basic.