Whilst it's correct that green wood bends most easily, my preference for steam bending is material that's been dried to roughly 20%±2% MC. This is because if very wet wood is bent, i.e., wood well above FSP with significant quantities of liquid in the cell cavities, the bending can cause bursting of the cell walls as any fully charged cells compress and disrupt. Such disruption leads to unnecessary loss of strength in the wood, which is undesirable. There’s less cell wall damage caused during the bending process if there’s ‘wiggle’ room inside the cell itself due to it being empty—the condition found in wood below FSP.
In addition, compared to green wood, wood dried to ±20% MC has had chance to reveal some of the distortion, checking, splitting and other faults the drying process can cause. Selecting fault free air dried parts for bending means they are likely to go through the heating, steaming and wetting process, and the subsequent re-drying and cooling after bending with less risk of those faults showing up in the finished bend.
As to the question of best grain orientation for bending it's much more common for growth rings parallel with the bend rather than perpendicular to it. I think the reason for that is prosaic rather than for technical reasons in that tangentially sawn material is much more common than radially (quarter) sawn stuff. There are times when sapwood should be on the convex side of a bend. One example is the yew English longbow which, when drawn to shoot, i.e., temporarily bent, where the sapwood has good ability to cope with tension better than the wood's heartwood which copes well with compression (the belly side) and thus faces the archer in use. Apart from that specific case I can't think of other circumstances where the bark side or the pith side should be on the concave or convex side of a bend, which only means what I say, i.e., I don't know, and there may be circumstances where it matters. Slainte.