The boiled bamboo shoot I bought at a near-by Japanese grocery store had "Himekawa" 姫皮 attached (left image). Himekawa is the very soft top inner part of bamboo shoot. I removed this first and cut it into strips. I was initially thinking of using this for a different dish such as a Japanese "ae-mono" salad but I got lazy and decided to use it in this dish as well. I added "himekawa" to the pot just before serving to warm it up and season. You need not really cook this part further.
I cut off the lower 1/3 (I intended to use the lower part for other dish) and cut the top portion in quarters lengthwise. Then I further cut it into small wedges. You may find chalky white stuff between the segments of bamboo shoot. This is an amino acid (tyrosine) congealed. Tyrosine is not water soluble and is contained abundantly in the bamboo shoot itself. As such, it is not harmful and OK to eat but, for a better presentation, you may want to wash off most of the visible ones.
I put dashi (1 cup), mirin (1 tbs), sake (1 tbs) and soy sauce (2 tbs) in a small pan on medium flame. If you want to keep the light color of the bamboo shoot, use a light colored soy sauce or "usukuchi shuyu". When it comes to a boil, turn the heat down to simmer. I cook it for about 20-30 minutes or until the cooking liquid is reduced in half. Just 1 minute before serving, I add "himekawa" and hydrated wakame to warm them up but not really "cook" them. To serve, I first place the wakame (left, back in the above picture) and "himekawa" (right, back) in a sallow bowl. I took out the cooked bamboo shoot in another bowl and added bonito flakes and mixed to coat (optional) and served them next to the wakame and himekawa as seen above.
For dried wakame and vacuum packed bamboo shoot, this was not bad. We had this with cold sake as a second dish after we had the avocado and tunas sashimi cubes, a very nice contrast.