You can't keep bare rooted trees "waiting for a season or more". Moving trees with bare roots is an effective technique (and cheap if you want to transport them long distances, because you aren't moving lots of heavy earth along with them) but as soon as the weather starts to warm up they will start to grow, and if they are not planted by then they will die within a few days.
The two essentials are (1) keep them dormant and (2) don't let them get dehydrated.
For (1), the important thing is temperature - i.e. cold. Don't keep them indoors. Temporary planting in the ground is a good way to keep the roots cold, as well as providing moisture. Ideally, don't even think about digging up bare rooted trees to move them until after two or three nights of hard frost, to be sure they really have "switched off" for the winter. In most of the UK, right now (November) is probably two months too early in an average winter. The only time when you can't dig them up or plant them is when the ground is frozen hard - not because it would damage the trees, but simply because you can't easily work with frozen earth.
For (2), keeping the packing material round the roots damp can work, but the problem is that you don't really know how well the roots are in contact with the material. Planting them in something similar to earth makes sure all the roots are in contact with a source of moisture. Also, while they are still in their packaging, keep them sheltered from wind and sun to minimize water loss.
The traditional method is to dig a slit trench and plant them in that. So long as you don't damage the roots, there is no need to be over-careful about this - just make sure the roots end up surrounded by earth, and not in air pockets. They are not going to grow, so you can pack them in like sardines - there is no need to space them out as you would when planting them permanently. It's quite OK to "plant" them leaning at an angle of 45 degrees or more, so the roots will fit into a shallower trench.
If it isn't possible to do that and you want to use a material other than soil, mulch or compost is just a waste of good mulch or compost - you don't want them to start growing, so there is no point providing any nutrients! Sand may be abrasive, and doesn't retain water in the same way as soil - the roots will either be in liquid water or air, neither of which is good. Wood shavings might work, but they may be too coarse to be in good contact with the roots. Sawdust would probably be better. If you have "loose fluffy loamy soil", just planting them temporarily in the soil will be easy, so why dig up the soil to fill a container or whatever, and make more work for yourself?
Whatever you decide to do, do it quickly. Leaving a bare rooted tree lying on the ground with no packaging around the roots for a couple of hours on a nice sunny and breezy winter's day, while you are digging the final planting holes or whatever, WILL damage it. It probably won't kill it, but it may spend the next year recovering from the shock, rather than growing strongly.
