small bulbs, I compost. No question.

Large bulbs, I keep in a cool, dry spot in my gazebo until fall when I plant the bulbs. I keep the tops on the plants until they are dried and shrivelled. If you have a colour reference, that is even better.

Sometimes, if I am not cramped for space, I will plant the bulbs and stems immediately, and wait for the leaves to shrivel and dry. That works well, and then you have the bulbs already in place for next spring. Squirrels sometimes do some rearranging, as well as snacking.