It is best if the bottom of the bulb is a fraction above the water. The roots will not rot, at least on mine they never do, but as soon as the flower is finished I plant mine straight out in the garden. Maybe that's not possible in your zone in the winter.

Thank-you for the response. I can not plant into the garden until April or so, but I wonder if I should pot it, or experiment with how long it will live in the jar?

All the time the leaves are growing the roots shouldn't rot, even in water. Here's another posting on hyacinths in water I've put some pictures on.

Here is a link that might be useful: Hyacinths in glasses

Thank you for showing me the post of the more detailed instructions. We are way below freezing here and the one that I purchased while in bloom is now done. It looks as though the leaves are now dieing back and the water has clouded in the vase.
The place I bought it from said that I should now store the bulb in the root cellar until Autumn and plant it to come back next Spring, in the garden.
I noticed that you do not have pebbles in your vases, only water.

No, no pebbles. If you have the special hyacinth glasses the cup shaped top means the plants do not fall over. Maybe in other vases the pebbles are needed to keep them upright?

The one I bought was in a bluish vase exactly as the ones in your picture and it also had the white stones. I just assumed they were necessary, perhaps for breathing and continued moisture while letting the water go down. Evidently none of these measures are necessary.

I'm so used to roots needing air and water that I was fussing over this bulb quite a bit. Learning all the time. Thank-you. :)