I pot mine up inside in a couple of weeks and give them some water. That way they get well established before moving them outside.

I've had 3 inch bulbs bloom, but the flowers were smaller that first year. But I would think that they are large enough, something else must be going wrong. I've only grown them in pots - mostly to protect them from voles. I grow Sulfur Queen which is a hybrid. In general in this group of bulbs - every cluster of four leaves makes one bloom stalk. If your leaves look healthy and you have more than four leaves then you should be getting flowers. The only thing I can think of is winter temps - either its too cold for this particular bulb or its not cold enough where you live. You need to find out if anyone near you can get them to bloom in the ground. Around Raleigh they are reliable but eventually they seem to fade away.

Cora, are you thinking of Crinum pedunculatum? That is a different plant - leaves grow pointed and upright. Overall it is a much "tougher"-looking plant. They are planted all over by the city at the beach. Link to images below. Peruvian daffodils are softer and more gentle-looking. They have leaves similar to an amaryllis or agapanthus. Here is a link that might be useful: Google Images of Crinum pedunculatum

Lin, Hymenocallis galvestonensis sounds like it would be fun to grow, but it says below that it doesn't like alkaline soil so unfortunately that lets me out. Oh well, it would be great for those with acid or more neutral soil than I have. This was on the D garden site; "On Aug 12, 2006, dmj1218 from west Houston, TX (Zone 9a) wrote: The controversial identification of this native plant was finally resolved in 1995 by Thad M. Howard. It is native to East Texas, Arkansas, southeastern Oklahoma, western Louisiana, and southern Georgia in sandy upland soil. After the leaves disappear in late summer or fall, it produces tall, naked scapes of white flowers in Lycoris fashion. The scapes of H.galvestonensis is round or oval in cross section. The seed is large, somewhat rounded, and pale green. The leaves are wider than other Hymenocallis species and the tips of the leaves are blunt, rather than pointed. It does not tolerate alkaline soil."