I use .22 short, .22 long, .22 CB long and Remington CeeBee .22lr for plinking in the woods without drawing too much attention. They are hard to find locally (for me at least) so I always buy whatever I might find at the LGS. The Remington CeeBee .22 was I think $9 for a box of 100 last time I bought some, which is kind of ridiculous but I like those rounds. It's slow shooting out of single shot bolt action .22 rifle though.
Good luck in the search.