Standard potting soil like
miracle grow will serve the porpuse.

However, in northern climates like Massachussets and mine here in Michigan, wintering is an issue -- many perennials which are perfectly hardy in the ground will not overwinter successfully in an above-ground, exposed container, since the soil is subject to all of the cold of the air, and will freeze and get much colder than soil in the ground, which never actually gets too much below the freezing point in our climate. Further south, this type of thing would not be an issue.

You can do one of several things: bury the containers up to rim in a sheltered location and mulch (which is what you don't want to do because of your rocky soil), push the containers into the most sheltered corner you have, preferably up against the exterior wall of a heated room, and mulch extremely heavily both on top and on the sides, to trap the escaping heat from the building, or move the containers into a barely heated space like a garage, if you have such a place, where they won't freeze deeply.

Just so you know, I've been able to winter the ornamental asparagus like sprengerii and plumosa by cutting the tops off and storing the pot dry in my basement in complete darkness all winter -- the plants grow long, stringy, yellow shoots, but I just cut those off in the spring, take them outside, and water, and they bounce right back. I don't know if this approach would work for vegetable asapargus, since it is a temperate zone plant and the ornamentals are tropical, but I suppose it might be worth a try -- who knows, you might be able to grow the expensive white asparagus by this method.

Hope this offers some guidance.

Dennis in Michigan

I thought about bringing the container into my unheated basement during the winter. Would that suffice? I grow mushrooms down there during the winter, and it very rarely gets above 65° during the coldest part of the year (January-February around here)

Yes, is suspect it might work, based on the somewhat tuberous root system of the asparagus, the ability of many of its relatives to go into a dormancy due to drought, as oppossed to just to cold. I suppose you wouldn't be out much if you bought a package of roots from a discount store or chain store in the spring, potted them up, and brought them into the basement in the late fall next year.

Could you elaborate more about the mushroom cultivation -- varieties, methods, media used, results?

I usually just buy a mushroom kit from any catalog I see them in. They are very easy to use. You mix the bag of compost w. water, and spread it over the mushroom spore. Cover it up for a week, and then open it and mist it as needed. When stored in a cool, dark location, they will produce shrooms for up to 6-10 weeks. My wife goes nutty over plain old button mushrooms, so that's what I get

Here is a link that might be useful: Mushroom kit

I use Miracle grow for the potted plants like Murraya koenigii,Grand Duke of Tuscany,Bell of India , Moringa oleifera (Dwarf) and Indian Borage(Same as Spanish thyme).Pots are easier to take in the house in winter. 65 degres should be O.K.