Rick, Sorry to hear about your problems. So did they debit your account for all 9 times or only the last try? Not sure if the amount being contested is worth the trouble while you're trying to enjoy a holiday, but see if you can escalate this with their local branch manager (was the ATM located at at a branch)? Don't know how feasible it is, but if you still have your slip or know when the "transaction" took place, maybe they can cross check their ATM security cameras and ATM records. Or at least lodge the complaint with your local bank as soon as possibly so it can be contested when you get home.
I've personally used BCA (Bank Central Asia - one of the largest Indonesia) ATM's across the country without problems. Along with Bank Mandiri (largest gov't owned commercial bank), I think you'll find these two most frequently due to their size and national coverage.
Geoff, off hand, BCA, Mandiri, BII (Bank Internasional Indonesia), Panin are decent local banks. I would just suggest using ATM's that are located in major shopping areas or attached to branches and of course, obviously those that have signs for Plus or Cirrus

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In my travels around Asia, I haven't come across any ATM problems other than just the cases where the local network isn't connected to Plus or Cirrus. But I do admit, where possible I'll try locating a HSBC or Citi branch. Not sure if HSBC Indonesia has a Bali office (they do have a presence in the Jakarta area but that doesn't help you...)