Ask Mr. Smarty Plants

We are going to quote from the webpage on Eustoma exaltatum ssp. russellianum (showy prairie gentian) which has propagation instructions (at the lower part of the page).

"Propagation Material: Seeds
Description: The seed is exceptionally small and somewhat difficult to germinate. The best results have come from surface seeding (since the seed requires light for germination) in flats at approximately 70-75 degrees. Field seeding can be done in spring or fall, however, spring germination usually results in the vegetative growth overwintering and not flowering until the second summer. Fall germination should produce flowers the first season.
Seed Collection: Collect seed in June, when seeds inside Capsule (A dry fruit that splits open along three or more lines.) are black.
Seed Treatment: The seed for E. grandiflorum is not commercially available, and thus, no large-scale seeding rates have been established. Note that the seed is exceedingly small-one capsule can produce 1200 seedlings!
Commercially Avail: yes
Maintenance: When the seed capsule ripens (in September or October), the stalk should be cut back to 2 3 inches above the ground. By mid September, the base will develop a cluster of 8 to 10 new shoots. These will remain as a cluster of leaves throughout the winter and resume growth in the spring. Plants that overwinter are usually much stronger and have more flowers than they do the first year."

You will note that this has instructions for both seeding and for over-wintering the plants you already have. As to why you have plants and your neighbor has had them and now has none-this could be the result of your neighbor mowing his land, or at least cutting everything down, at a bad time for the bluebells to come back up. Maybe you have had bluebells trying to come up and you have been mowing too often in the past. And, yes, the seeds could have blown to your land, but as they are so very small, that probably is not the sole explanation for your having a stand this year. It may already be a little too late for gathering the seeds, but you can at least look at the seed capsules. Remember we told you the seeds looked like black pepper. We would suggest a combination attempt. First, try to preserve the plants you have by following the instructions in Maintenance, above. Make an attempt to gather seed, and store it in several different ways, to see which way works best. In the Fall, plant them in flats and see how many you can get to germinate. Plant the baby plants out in the Spring, on the same kind of ground as your existing plants are growing. Keep records of when the seeds were planted, and how they were stored, so you will know how to do it better next year.

Here also is our How-To Article Seed Collecting and Storage to hopefully add some more information. And, finally, this Virginia Cooperative Extension article on Plant Propagation from Seed.