My Mom (no insurance) shops around as follows: "Hi, I'm told I need X done, but I need to know the price. I don't have insurance, and I want to make sure I have enough money to pay for it."

She tends to get accurate estimates, probably because hospitals don't like to hear "I thought it only cost $X, I don't have $X + $Y, so, umm..."

Granted, what she gets isn't likely to be a "a complete cost estimate [...], [...] reflective of any negotiated discounts, [...] inclusive of all associated costs, and did not identify consumers’ out-of-pocket costs", which is what the GAO wanted. But it's certainly good enough for shopping around.