What bike do you have?

It sounds like it was not fitted properly for you. A hard seat is not necessarily bad. Soft can work over short distances, but you need support of sit bones. Have you tried stretching? Part of the problem may be flexibility as well as fit. I'd suggest getting your fit optimized for riding on the hoods and then later get it readjusted for riding in the drops, after you are more accustomized to the new bike.