No, you don't need cave or cavern certifications to dive there. Bonne Terre is a flooded mine, but it is more like a huge lake in a bigger cavern. There are overhead areas that they will take some divers through, but those are on the much later & more experienced trails.
From the descriptions I've heard (never dove there myself- please correct me if I am wrong), it is $65/ dive- 2 dives minimum to dive there. You are taken on guided dives along several "trails". Dive lights are not allowed, as the palce is lit up anyway. Any "dive packages" they have comes when you stay in their lodging facilities. I think they have packages w/ lodging for 2- 5 dives over a few days. 58 degrees is definitely towards the drysuit side, but can also be done with a 7mm semi dry, or a 7 mm wetsuit. Mostly depends on how sensitive you are to the cold.