LILINEWCAS, it's perhaps not the best angle to assess height from, but your lily looks rather short? I suspect this could be a dwarf Asiatic lily called 'Tiny Padhye'.
It's of course possible that there are similar cultivars, although this is a lily with a rather distinctive look.
As for how large your bulbs need to be to flower, well it depends on what cultivar you have gotten. Generally speaking Asiatic lilies flower from smaller bulbs then Orientals and so on. I think you probably got Asiatic or LA lily bulbs as they usually are quickest to increase. If we were to assume the bulbs you received indeed are Asiatic bulbs, they can flower from rather small size, especially the dwarf growing cultivars. For instance 'Tiny Padhye' are sold from 10-12 cm bulbs and they should already give several flowers
http://www.vws-flowerbulbs.nl/.... Probably it could flower from even smaller bulbs, but if they really are "very tiny", then I think you will have to wait for next year. Asiatics grow quickly, on the other hand other types of lilies can be a lot slower to grow. Also of course it depends on how well you grow them.