There's no such thing as white moss - sometimes bags of compost or the like do have green moss growing, or algae, usually on the outside edges against the bag wall, but this sounds more like fungal mycelium, the root threads for mushrooms. Its very common on wood chips, quite normal, and won't be visible once exposed to the air (it'll still be there, but will retreat to a darker place beneath where you can't see it), but you might find you get mushrooms or toadstools at some point during the year - or not. Harmless to your garden and plants.

Thank you for your answer, much apprecciated