One of the things I dislike intensely about paeonies is the fact that their flowerheads are so heavy that they do droop without being staked to keep them up. This, though, usually happens as the flower opens and gets large, rather than when it's at the bud stage, so not sure this explains what's happening with yours.

is the bud stem actually withering and shrivelling? that sometimes happens and is due to the weather conditions really.

The stem of the plant is fine. In fact all of the plant looks very healthy, but the flower bud and the bud stem is bending earthwards! It looks like flowers in vases look when they've gone past their best.

There is another thing about peonias. They don't bloom as well if the crown is too deep. They apparently like to be near the surface. Planted shallow. No mulch near the crown, compost near to crown, or burying to frost protect. I only have room for one Bowl of Beauty. One year our garden help put compost on the crown.....no flowers that year. This year counted 20+ buds so far after moving soil off crown in autumn. might help with the drooping too...or not.

Thanks for all of your answers. Yesterday I scaped some of the soil away from the crown and then gave the soil and a very good soaking. Something seems to be working because the bud is definitely straightening up.