I grew some in a compost bin last year and they turned out fine! I used Carlingford seed potatoes. There is no harm in trying out different things to see what is best for your situation.
When should I take them out of the bin. I have read that they should be take up as soon as the flowers die. Surely they can be left in until the stems blacken, or will they rot in the drum?
i never heard of this before now! potatoes in a bag, what a neat idea! usually what i do for potatos every year is to find someone i know that doesn't mind parting with a couple of bales of hay, about 4 to 5 of them. i place them at the edges of the garden and dig out the center from the top, then fill with layers of composted dirt and potting soil and plant my potatoes in there. when they are ready to harvest i just untie the bales in the morning and let them "settle" for the day, they are really easy to tear apart and get the potatoes from, and then i can use the extra hay for mulching my strawberries and bedding them in for the rest of the season, since they have long since given up their fruit for the year.
I have just done something similar. I made a 4ft square raised bed made from an old scaffolding batten, with 2x2 timber post in 2 corners. took the 2" turf/weeds off the top, put a little seived soil in and added my potatoes and soil. As they sprout i will add another level of planks/soil and keep doing the same, until i get approx 4ft high.
then when ready just remove the boards one by one and reep the crops, i got the idea from another allotment owner who used old tyres !!
Your idea sounds really great. i am going to try it next time around. So far my potatoes are doing really well. As they shove up through the surface I have continually topped up the level of compost/soil mix. I'll just have to wait and see what comes out!