A peat bog is a much worse place to try and rot moss than your compost heap. If your compost heap failed to rot it, it is because it is too much like a peat bog. What peat bogs do is prevent stuff from rotting, by excluding air, as in the preserved bog bodies we find from time to time. That's why you can still make out the original moss remains in peat, though commercial peat may be ground up so you can't see it as well as in a bog itself. In practice the preservation often isn't perfect which is why peat is defined as "partially decayed vegetation".

A large mass of moss in your compost heap can act as a plug to exclude air, which prevents rotting in the same way as a peat bog so you need to mix it up to get it to rot.