Tire disposal is part of the installation package price when I get new tires, but for other things like my riding mower, there's a recycling program that accepts them (among other large things) for free a couple days in a row every year, so I just hold onto them until then. I mean because I mount them myself, if I were having some shop/dealer do it then I'd just pay them the ~couple bucks to dispose of them.
What a ripoff my local lawn mower dealer is, not only did they want $30 to mount tires (can't recall if it was for 2 or each tire), they also wanted 50% more for the tires than I could get same for online including shipping, almost $100 each.