Played a round yesterday and rode in a cart. Driver/hybrid headcovers usually got tossed in the basket before each shot.
Putter cover had much more variety. Placed on the alignment sticks sometimes, shoved halfway into the bag others. Any time I was off the green on my approach however, putter cover stays on and it just goes on the ground with the wedges while putting.
Friend had a different but efficient method, putter cover is tossed on the ground just outside of the cart while walking to the green so he was to walk over it on the way back.