I think it is fine to ask the price ahead of time, but I confess to very rarely seeing it done and only for unusual items like a high end scotch or wine. Once you find out, you can either decline or accept the price. The price changing is odd, but the polite response is not, it's wrong, but something along the lines of could you check again, I only paid X last time I ordered it. If you are 100% sure of the price, sure enough to correct the bartender, why ask at all?
Once you order it and the drink is made, I think you are obliged to pay for it, even if you ordered the wrong drink or the price is more than you expected. I suppose there is some practical limit to that, but the price would have to be much different than the norm. The exceptions for me would be if the price were posted and they refused to honor it or it changed drastically from one drink to another in the same night, excluding a happy hour or similar promotion ending. It's fine to ask about a change in price, but there is always the possibility they made a mistake on the first one.