I've been fairly vocal about the positive benefits of using locally invasive species for Bonsai. Biggest benefit is that property managers, like park rangers, etc., will give permission to dig up invasives, where getting permission to dig natives might be near impossible.
There is a "local" component in dealing with invasives. For example, pre 1491 both black locust (Robinia pseudoacacia) and Osage orange (Maclura pomifera) had fairly narrow distributions, only found in one or two states of USA, but both have been planted widely post colonization and now both are common, and especially the Robinia somewhat weedy or invasive in 40 or more of USA states and they have expanded into southern parts of Canadian provinces.
There are "nasty" invasive, like buckthorn, Rhamnus cathartic, that has dense shade, shading out all competition, and its roots alter pH of soil, raising pH, and exuding an allelopathic chemical that inhibits other tree species roots from colonizing same plot of soil. Factoid: Buckthorn was introduced to the USA by a Scottish immigrant physician who settled in Glenview, Illinois around 1870. He brought buckthorn with him, because it reminded him of Scotland highlands. In Scotland and Europe, Rhamnus is reasonably well behaved. It became a "thug plant" in North America because the different soil microbiome species made new partnerships that supercharged the buckthorn's metabolism. Buckthorn in North America is much more vigorous due to a different group of species of soil mycorrhiza and bacteria. Talk about unintended consequences.
Many species snuck in as weed seed mixed in with crop seed. Many others were brought in for use as landscape plants and escaped. Norway maple, Acer platanoides is everywhere in my area, and has replaced the sugar maple in our little patches of forest preserves. Fortunately our EU members have a number of threads showing Norway maple is good for medium to large size bonsai.
Another group are the "not too weedy" economic escapees. For example apples are not native to North America, but now can be found everywhere, usually as relics of previous orchard plantings, but some reseeding in hedgerows. Apples make great blooming bonsai. Remember fruit size tends to stay constant regardless of size of tree, so limit the number of flowers you allow to produce apples if your tree is small. Pretty much most of the genus Prunus in commerce is introduced from Europe or Asia, though there are a very few NA native Prunus. Some can be used for bonsai.
Key is for "outdoor Bonsai" use species that grow well in your neighborhood or in the colder neighborhood just to the north of you, assuming you are north of the equator. Often the most vigorous trees locally are indeed the invasives.