What do I do with a bucket that's about a quarter full of some kind of cleaner or chemical?

Well it's a tough call with a couple of answers. You don't have to like all my suggestions I'll just throw them out.

1 - Bad idea to put down the drain even diluted. So scatch that one.

2 - You could use it on an area where you want weeds to be killed or around pavement where you want a small blank strip of grass.

3 - If you are in a rural area in most cases you can burn it. That's not enough material to cause toxic dropout.

4 - Check in your area for where they take paint can disposals. Put it in a can and dispose of it that way.

5 - Oil recycling center may take it.

6 - Talk to local hardware store just say you have some used paint thinner and need to get rid of it.

Contact your trash pick up service of your town. Most towns today have special place to bring such items. In Ft Worth TX if they can be identfied they are put in area for free pick up by other persons to use and others are disposed but I dont know where. *mamatx

Call the local waste disposal, they might not take it but they can direct you to your local Household Hazardous Waste Disposal unit.