I want to make something like this vase made from an incandescent light bulb:
But I wonder what kind of grass can I put in which will not rot?
While there are grasses that grow submerged or partially submerged, the picture you provided is not one of them. Your picture depicts a bouquet arrangement. It may be very simple and only include grass-like leaves, but that's all it is. Like putting flowers in a vase.
Spider plants (Chlorophytum comosum) will grow in a vase. I even have some growing in yogurt cups which are roughly the size of a light bulb. My baby spider plants (harvested from a mother plant, not seeds) seem to do just as well in plain water as in soil. The only noticeable difference is that the water-based plants have somewhat less fleshy roots than the potted ones. They don't rot per se but aging leaves will go brown as with many other plants. Just keep most of the roots underwater, and replace the water every couple weeks. If no baby spider plants are handy, it is probably possible to rinse off a potted mature one and move it into a vase. (I haven't tried that but spider plants are relatively durable.)
Rice is a grass that famously can grow in water, at least for a time. Rice roots will suffocate and die in water, but new roots sprout just above the water line in the process.