Dying my hair super blonde?

I'm sure someone more experienced will come along and answer so in the mean time, I'll give my 2 cents.
What you'll want to do first is get a color remover for the permanent dye. You may have to do it more than once, and make sure to rinse and follow the directions carefully so it doesn't re-oxidize. It's not damaging, but it can be drying so you'll want to add moisture to your hair afterwards.
From there you can see how light of a base you're left with and can proceed with bleaching. You can do full strength bleaches no sooner than one month apart or more frequent bleach baths to get you to the level you want. You can tone from there or use a silver/blonde shampoo to remove excess yellow tones.
It seems like you're wanting to go to a salon to get it done, so I'm sure each stylist/colorist will have their own method of doing it, but if you want your hair to be as healthy as possible I would suggest following the advise of the people on this forum, they really know their stuff. Personally, I wouldn't let a stylist put bleach anywhere near my head, but I'm sure some out there can do it relatively safely and know what they're doing, I'm sure the stylists on here would do an excellent job. The cost probably varies from stylist to stylist, and doing your roots will depend on how quickly they grow in. I do mine about once a month. It seems to me like you just need to call around and ask, but maybe there's a rough cost estimate someone can give you. Good luck 🙂

If you must go to a hairdresser, do use colour removers before going. Many hairdressers don't like colour removers and swear they're bad for your hair and then proceed to bleach out colour, which actually is a terrible way of doing it. Get rid of as much of the dye as you can, then go.

I'd much rather do the bleaching myself as well, and do in fact 🙂