We've used Tiger in the past (I often see a driver waiting in the parking lot at Leverick), but we haven't done the baths in a couple of years, so I'm not sure what the current charges are.
My understanding (not from personal experience) is that to avoid the cruise ships, going super-early is generally better.
But my personal recommendation, if you have some schedule flexibility, is to look at the cruise ship schedule and plan your Baths visit on a day there aren't cruise ships in port. I find I can usually make this work without derailing our planned itinerary by simply changing the order in which we do Leverick, BEYC, and/or Saba.
Hope that helps.
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