Inflateable ring or metal frame pool? Either way, bark's probably not a good foundation for a pool. It will waterlog and rot leaving shifting base. Sand may be OK for a inflateable ring pool if it's contained and won't wash away. The legs on a metal frame pool may sink into sand.

Since you're willing to do the work and rent a compactor, how about crushed concrete, QP (Quarry Product - thanks CarlD), or base material for a paver patio compacted level? You'd still need a layer to protect the liner