If you insist on using a colon instead of a comma with a dialogue tag (even though it’s jarring and very much nonstandard to do so), do not use said or any other speech verb with it; just use the character’s name or whatever, followed by the colon.
Dialogue belongs in the same paragraph as its tag.
Post-apocalyptic needs a hyphen.
The rest of the changes I’ve made to this example are for improving flow rather than correcting mechanical errors.
You are a scavenger and have lived your entire life in a post-apocalyptic wasteland.
One day, you stumble onto a bunker and open it. Inside is a friendly looking woman.
She adjusts her reading glasses, brushes the dust off her apron, and says, “Oh? Is it safe to go out on the surface now?”