Cleaning Litter Box

Hi. I would appreciate any suggestions to my question
I scoop out my buddy's cat box every day but am having
a bit of a problem about how to discard the clumps.
If I have a garbage bag that is ready to go out I'll dump
the clumps in it but if I don't I put the clumps in a gallon
size zip-lock bag, seal it and throw it in my kitchen garbage.
I'm sure there's a better way and was hoping for some suggestions.

Thanks in advance,
James