All steroids have the potential to weaken bones, hydrocortisone as much as prednisolone, especially if you are on too high a dose. Why were you changed to prednisolone, were you not well controlled on the hydrocortisone? If so, ovarian cysts are usually due to undertreatment/poor control, so maybe these are a result of the hydrocortisone?
A lot of adults are changed to prednisolone, mainly for convenience as you only have to take it twice a day, which is easier from a compliance point of view. I personally don't think it is worth changing for that reason alone though and if a patient is well controlled on hydrocortisone, they should have the option to stay on it and most endo's agree with that too. Prednisolone is a lot stronger and stays in the system longer, so if the dose is too high, it could cause side effects such as weakening bones over time. However the same is true hydrocortisone, if the dose is too high, so really ensuring you have the appropriate tests to determine the right dose of either medication is fine tuned to your exact requirement is vital.
Sorry to hear you have had problems Lisa but hopefully now you are back on treatment that suits you and your bone density is recognised as low, you can build it back up in time and it will have no long lasting effeccts.