I would like to save seeds from my double lavender asters, I would like them to be pure, but I do not know if they will pollinate with wild ones. The nearest wild patch is about 100' from the plant. Bees go to all of the flowers. Do they cross pollinate too much to make seed saving worthwhile?
Generally, almost all members of Asteraceae (daisy family) are able to self-pollinate successfully and most species, including Asters, pollinate strictly by insects (A few species are pollinated abiotically, Ambrosia and Artemisia). You did not mention the color of the wild asters. Are they golden/yellow? If they are, you may be in luck. Some research has shown that the color of a flower is a predictor of when a flower will be pollinated. Lavender colors usually attract pollinators between September and October where as bright yellows attract between June and August (see bottom of page).
However asters do cross-pollinate (noted here under 'Propagation' and here under 'Faunal Associations'). So my best guess would be if the wild asters are similar in color (different shade of blue/purple) to your 'double lavender', you are out of luck. But if the wild asters are yellow/white/etc I would think they should be fine.
Good news: Some asters are perennial and propagate easily by division!