While outside, or in a well-ventilated area, add 2 parts water to 1 part bleach to the bucket.
To keep pinecones submerged in the mixture, lay bricks or large stones over them.
Let the pinecones soak in the mixture for 24 hours. Then, use your gloves to gently remove the bleached pinecones and place them on a roll of paper to dry out and allow fumes to dissipate.
It may take a few days for the pinecones to dry naturally. If you need them to dry faster, set your oven to the lowest setting and let them dry for a few hours.