Now obviously the most complete answer here would be to say "our data are decribed by a Gaussian of mean X and st. dev. Y", but people don't frequently do that in informal contexts, so how do you reduce it to one claim with one confidence?

My rule of thumb is to say I'm about 95% sure that the true value is within two standard deviations of the mean. It's usually a pretty good compromise, easy to reason with intuitively (try it!), and if your readers actually care about this you can always tack on a little parenthetical note that says "(Gaussian distribution, mean = X, std. dev. = Y)". Or stick it in a footnote, or whatever you can manage without terrifying your readers.