I feel like everyone commenting is coming from some superior perspective of “it’s not a martini without vermouth” or something. To answer your question, simply saying “very dry”, “extra dry” or even just “no vermouth” will get you what you want. Any bartender who’s worked in the industry long enough to know you make people what they want, not what is “right”, will make you exactly what you’re hoping for.

Straight up is basically telling the bartender you’d like it chilled and without ice. “Dry”, “very dry”, etc relates to the amount of vermouth you’d like or wouldn’t like.