Growing Asparagus In The Home Garden, HYG-1603-94
New research shows that harvesting in the second year after planting is fine--it stimulates more buds on the roots, resulting in more spears. You actually should not CUT the spears--instead, break them off where they snap easily, close to the ground. If you take them into the house and cook them there is no waste--no need to cut woody stuff off the bottom of the stalk, because you left that part in the garden.
I start harvesting mine when it is 8 inches tall or so. The first year you harvest it, stop harvesting when the spears get skinny as a pencil. Let all the rest of the spears grow and produce foliage to nourish the roots.
I have never heard of anyone growing asparagus in a container--I think that your pot is not big enough for four plants--maybe one? If you have any place that you can plant it in the dirt, it will do much better. Asparagus foliage is ferny and looks very pretty in a flower bed, if you don't have garden space.
Another thing, if anyone is interested in establishing a bed--don't spend more for 2 year old roots. The two year old roots are the scrawny roots that were not big enough to sell when they dug them at one year, so they put them back into the ground and let them grow another year. They are not much bigger than good healthy one year old roots. And if you plant one year old roots, you can harvest the spring after you plant them. You plant in spring--let them grow thru that first summer, pick the next spring.