My, you're getting a stout pranging on this one, aren't you?
Okay, driving late at night, not dressed appropriately for concealed carry (a bathing suit?), and wandering into the woods for urgent business. I'm with that.
As you've already noted, and been told, at a minimum, hide the handgun completely. I have a lock-box under my seat that protects my sidearm and provides a measure of security when I cannot have it on my person. I could actually envision doing this myself, late at night, in the middle of nowhere, where you don't expect passing traffic, let alone an investigation by Johnny Law. But you just don't know who you're liable to run into at the most inconvenient times. As you learned!
And more importantly, announce your presence immediately and let the officers know where you are. Why would you approach the police from the woods, from the dark, from behind?
No way I'm doing that. Hell, I'd hunker down in the woods and wait for dawn before I'd do that. But placed in your sandals, I'd announce my presence and ask the officers for instructions. Let them tell me just how and when they want me to pop out of the tree line.
Stay safe!