I have a three handle tub and shower faucet set from late 1950s. The cold water faucet was dripping and I managed to remove the handle and the bonnet nut. But I can't see how to remove the cartridge to check the washer and seat. Here is a snapshot. I don't see any other nut to unscrew.
All you need to do is put the handle back on the valve stem and turn it counterclockwise and the valve stem should unscrew out of the valve base. Removing the rubber washer that's shown there will make removing the valve stem a little easier. You can use a pair of pliers instead of the handle to remove the valve stem. Just be careful not to damage the the end of the stem or you'll have trouble putting the handle back on when you're done replacing the washer