It seems very early for your potato foliage to have died back, but unless the plant was blighted, and it's very early for that, the tubers should be ok left in the bag. After all, that's more or less the way you might store the tubers for winter. However, you might as well use the tubers up now as they won't grow any bigger and will be at their best now rather than stored.
You can use the compost in the garden or just add it to your compost heap. In a hot heap any fungus or spores will tend to be destroyed. To be extra safe, don't plant potatoes or tomatoes where you spread the compost, but I must admit that wouldn't worry me. You could also use the compost safely next year by sieving it and mixing it with some fertiliser granules for pot plants like geraniums or other flowering plants.