Best not to plant straight into pure farmyard manure, they'll do better in decent potting compost, maybe 20% John Innes and multi purpose mixed. You can buy this at the garden centre already mixed up, if not buy both and mix them yourself. I'm saying 20% JI because its loam based and can be heavy once wet, likely too heavy for lighter bags than the one you're showing in your photograph, especially if you need to move the bag.
I can't tell if you made holes in the bottom of the bag you used, but I can tell you didn't add compost as the green tops grew - it should be topped up so that only the green tops can be seen. I also don't know whether you chitted the potatoes before planting or what variety, so actually, I don't know very much at all about what you have done!
There are two links below - one is to Thompson and Morgan and its just for interest's sake, I'm not recommending any T&M product nor their potatoes, but they say they have trialed filling the bags up to the top with compost prior to planting the potatoes and had success with this method, rather than the method described in the second link, which is the more usual way of doing it. I can't recommend one or the other, never tried with a bag full of compost, but it might be worth experimenting yourself to see which works best, or at all.
Watering is very important - you need to make sure they have an even and sufficient water supply, but check frequently to make sure they're not too wet or they'll rot, particularly if out in the open and exposed to rain. You may need to cover or move under cover if the weather is wet for an extended period. The reason watering's important is, if the water supply is erratic, you will finish up with 'powdery' potatoes, meaning they'll turn to powdery mush when you try to boil them, even if they're a variety that are meant to be fairly waxy and good for boiling. In terms of drainage, they drain better if not straight onto earth - I used to stand mine on old grill pan grills balanced on bricks (any close spaced rack that's big enough will do) to allow better drainage. Not pretty to look at, but effective.
I'd just add something else - the bags you use should really be black and fairly thick (think heavy duty black rubble sack) - the idea is to exclude light from the tubers as they grow, and its harder to achieve that in light coloured bags. If you don't exclude light from the tubers, they start to go green, and at that point, they're toxic and should not be eaten. That's why you store them in the dark after you've bought them or dug them up - it should also be cool to deter any possible chitting or sprouting if they're meant to be eaten.
Also note I am in the UK, which means I know what you mean by the term 'compost', except I'm not sure what you mean by 'standard' compost - I'm assuming you mean potting rather than garden compost from your heap or bin.