I haven't seen these things in the markets here. How do I ask for them in the local market?
"Baans" (बांस) is the Hindi word for bamboo - there does not appear to be one for the edible shoot. Instead, there are a number of words used in Indian cuisine for bamboo shoots, depending on region.
In Mizoram, they are called 'Mau Tuai/Raw Tuai'. In Manipur, the fresh bamboo shoots are called 'Uusoi' and the fermented bamboo shoots are known as "Soibum". In Nagaland they are called bas-tanga. In Assam, they are referred to as gaz and in Nepal as tama (Nepali: तामा). In western orissa region of India, people call it kardi and it is the most famous dish there. In Jharkhand, they are known as sandhna
Wikipedia article on Bamboo Shoots.
Bamboo shoot tips are called salad or simply sunjian in Chinese and juk sun in Korean, mang in Vietnamese, take no ko in Japanese, gaz in Assam, tama in Nepal and kardi in western orissa. Bamboo shoots are eaten in Goa usually during the monsoon season and are commonly known as Kill. Bamboo shoots are used in preparing curries and pickle in the state of Jharkhand, India. In Western Orissa or the Kosal region of India, it is a common ingredient. Since this region is dominated by the tribal population, bamboo shoots (or “kardi” as it is known), is believed to have been in use for hundred of years. In this region, “kardi achar” (pickled bamboo shoots) and “kardi baja” (fried bamboo shoot strands) are also popular.
"Bamboo Shoots" - by Sanjay Summa on the Vah Reh Vah site.
Keerl (bamboo shoots) is something you will either love or hate.
"Keerl Ani Moog Sukho" - by Shireen Sequeira on her Ruchik Randhap blog, devoted to Mangalorean cuisine.
Kalale and Kanile are the names given by the Bhakshya Bhojana blog.