I haven't grown in a bag, but due to having a low lying garden with soggy ground in the spring, I tried the method of growing them in a circle made from hog wire. using straw instead of dirt. They grew okay and it was pretty cool to just unhook the ring and have all the potatoes roll out. On the down side, the skins were really pale yellowish. I guess because there was no minerals from the soil? The color was offputting. So last year I went back to regular rows, but alas, once again almost all of them rotted when the monsoon set in. Anyhoo, I think good production is considered five pounds of new potatoes for one pound worth of seed potato. In my view, there are much better/profitable use of your limited space. Potatoes are cheap in the grocery store relative to things like peppers, cukes, tomatoes. I'd even try a little french melon instead of potato.

I only have 1 year experience growing in bags...here is my advice.
There is no benefit to staggering plantings. You may plant an early and late variety to (somewhat)accomplish your goal . Potatoes do not ripen suddenly and it is actually good to leave them in the ground to toughen the skins. You will not be dealing with this growing in bags because you will have to use all of your will power to wait until the vines die to harvest.
Use 15-20 gal containers
I used 1/3 compost 1/3 sand 1/3 perlite and that worked well as a soil mix. Put a few inches of soil in the bag before the tubers and then cover them with a few inches of soil and "hill" them twice as they grow by carefully adding more soil around the vines.
You can go to a good garden center and get seed potatoes in bulk so that you can buy the amount you need or go to a natural foods grocery and just but some that haven't been treated with retardant. For a 15 gal bag you will not need more than one or two cut into pieces.
Much has been written about this method. Google "growing potatoes in containers" and you will get too many hits to count. (google counts them for you)
GL.

Bintje is delicious. Probably my favorite, to date, for baking.

What you don't use this year, you should give to someone who will. They won't keep till next season.

George
Tahlequah, OK

I started a post on growing potatoes in containers and towers in the container growing forum last year that addresses some of your questions. There are lots of photos and several people shared their experiences. Follow the link below to check it out.

Here is a link that might be useful: Tale of two potato bins