car dealer change their mind on an agreed bill of sale

That's when you say No, or walk out and find another deal.

So bill of sales in CArGurus are not trusted and we can't flag bad dealers?

If you have a signed Bill of Sale you can hold them to it. Threaten to sue if you want.

Once the paperwork is signed both you and the Dealer are locked in. However, some States, like New Jersey for example, have a cooling off period for major purchases like a house or vehicle. In NJ it's 3 days. I don't think this applies to the Dealer, but you never know! Check with your local Department of Consumer Affairs to be sure. Hope that helps! Jim