Actually, you're just fine wiping down the base of the bullet onna rag.
A word of caution. Or words of caution. Mineral Spirits and Acetone, as they evaporate and dry, create HEAT. They can and will create enough heat to reach their respective Flash Points and spontaneously combust. SO:
NEVER EVER put rags with those chemicals in a can, in your house. In fact, take those rags OUTSIDE to dry immediately after use.