There are also “free living” bacteria that are capable of nitrogen fixing (diazotrophic), but are not as strictly root dwelling like Rhizobia. https://en.wikipedia.org/wiki/Paenibacillus

My company, Wilbur-Ellis, sells “Nutrio N-Tune” (https://www.cdms.net/ldat/ldJI1000.pdf) which contains spores of Paenibacillus Azotofixans.

Compared to the more well known legume colonizing Rhizobia bacteria, they can host on a wide variety of plant families. Our Paenibacillus Azotofixans can be applied to soil even before a crop is planted and does not need to be directly inoculate seed (though you can do so).

They also don’t seem to have their nitrogen fixing ability suppressed by nitrogen presence, so you can apply both them and fertilizer.

I’m told that under ideal conditions, their presence can behave like adding up to 0.5 pounds of nitrogen an acre per day. While they can’t certainly can’t replace fertilizer applications, that is an impressive amount, especially since it’s a constant source rather than whenever a grower can get around to putting something out.