What you're seeing is not uncommon when receiving bare root plants. The roots and buds you're seeing are perfectly fine to continue storing in a cool/dark place. The buds and roots would still be present, they'd just be hidden below the soil surface. The fact that you can see them is a good sign that the plant is healthy and alive. If you can store them in a refrigerator, that will provide the most consistent conditions. Around 40F is ideal for most bare root plants in storage. Be sure to check every few weeks for mold growth, that is not uncommon either. Simply remove any moldy packing materials and give a quick swipe with some rubbing alcohol to kill and spores (not too much, as alcohol can cause some desiccation, which you do not want). You want a good balance of not too wet, not too dry.

When you are ready to plant, this guide from Walters Gardens is pretty useful. This culture guide is for growing peonies in containers, but the information about temperature, watering and planting depth would all apply to planting directly in the ground as well. Planting at the correct soil depth is very important, so be sure to pay close attention there.

https://www.waltersgardens.com/culture_sheet.php?ID=21