Every winter we seem to have incidents in Mono County related to hot ashes. Sometimes hot ashes have even caught structures on fire, but more often the fire department is called to respond to smoking dumpsters from people who've poured their hot ashes inside. Neither one is a good scenario.
To properly dispose of ashes, you can get your own metal can or use a specifically-labeled one provided by your HOA (some condo complexes have them next to dumpsters). I use a metal can that I purchased at High Country Lumber in Bishop.
Every 7-10 days our wood stove needs to be cleaned out. I scoop the ashes from the stove and place them in the metal can. I let them rest in that can for 7-10 days. Once they're rested and I'm assured they're no longer "live," I then place them into our garbage can. I set the can outside until the next time I need it. If you add hot or "live" ash to a dumpster or regular trashcan, it can easily catch all the contents on fire and cause quite the scene.
Below is an old photo of my son (at 8 months old!) He loves the ash shovel. If I don't hide it, the shovel becomes his toy. Inside the stove are coals from the morning's burn. Ashes can easily stay "live" for 24-48 hours in a stove or metal can, so you might as well let the ashes sit in the metal can for as long as possible. If you have a garden, you can even save the ashes to use in your garden soil!