Particularly for unjacketed bullets like 22LR. Even jacketed bullets tend to not be jacketed at the base.
With rounds that aren't well jacketed like those 22s that are just bare lead, you also get some of the round scraping in the barrels that comes off as dust.
There's tons of lead in the air at shooting ranges.
Copper, polymer-coated, or total metal jacket rounds will also result in less lead on the firearm, I'd think, and less on the user's hands. One old guy I know who had lead poisoning at one time believes the real risk is getting the lead on one's hands and then handling a cigarette.