Chocolate is a sol, consisting of solid particles suspended in cocoa butter. It is something similar to a hard emulsion. And it can separate just the way a liquid emulsion does (think mayonnaise). This happens when you melt the cocoa butter completely, so the solid particles separate from the fat. If it happens to a chocolate bar, your chocolate looks grey. If it happens to a bowl of melted chocolate, the chocolate seizes the way you describe it. This happens with both milk and dark chocolate. If you haven't experienced it with milk chocolate before, you either had luck, or your milk chocolate was of a lesser quality than the dark one and contained non-cocoa fats and/or emulsifiers, which change the behavior of the sol.
The only way to prevent seizing is to work within the correct temperature zone, which is extremely narrow (2-3°C). Even as an experienced confiseur, it is extremely hard to judge it intuitively. If you insist on trying to watch the chocolate and guess when it is OK, you will have inconsistent results, with a seizing once every few tries.
What you need is to get a candy thermometer. Keep it in the chocolate and, whenever the temperature nears the danger zone, put the inner bain marie vessel in a basin of cold water you keep near the stove for this purpose. It will cool rapidly and stay tempered. It isn't a problem if you cool it off so much it hardens again; you can remelt chocolate as often as you want as long as you never exceed the seizing temerature.
And now for the numbers. All kinds of chocolate (milk, white, bitter) harden at 27°C. Between 27°C and 30°C, they are soft, but unworkable, because they are too viscous (hold unpacked chocolate pieces in your hand for a while to see what I mean). The workable zone is 30°C to 32°C for milk (and white) chocolate, and 30°C to 33°C for dark chocolate. Above this, your cocoa fat melts and the chocolate seizes. So, keep an eye at the thermometer, as you see, the zones are narrow.
Edit: I just noticed that you call 40% "bitter". This is a very low cocoa percentage, and I wouldn't let it go up to 33°C. The numbers for "bitter" are probably safe for 70% cocoa and above.
Real chocolate (cocoa solids, cocoa powder, and sugar) is not the best thing for what you want. If properly handled, it can give you a great tasting glaze - but you don't have the conditions to handle it properly (slow cooling), so you will run into problems with it (bad texture, sweating, bad looks/dull). Also, it won't be a really snappy shell. And at this temperature, the good flavor is not very noticeable anyway.
What you want to use is cocoa-containing fat glaze. This is the stuff which commercial "chocolate" coated ice cream like the Magnum brand uses. It is sold in supermarkets as "chocolate cake glaze" and similar names, but check the ingredient list to be sure. It should consist of cocoa solids and vegetable fat, possibly some emulsifiers too.
You should only melt your glaze, preferably have a low-temperature water bath at your booth (not full boil), and hold the glaze there for dipping. Don't add milk at all. Milk is a bad choice for chocolate covering anyway. Cream is used for making cake icings called ganache (mixed with real chocolate, not this glaze stuff), but it makes a soft, smeary icing, not a hard, snappy shell. Use the glaze the way it is, without adding anything.
This glaze is quite hard at room temperature already. A thin layer of it on a frozen banana should go to below room temperature almost instantly. I think you will have your shell without any special preparation. But I have never done it this way, so I would advise you to experiment. If my hunch is wrong, there still isn't anything you can add - this stuff doesn't harden because of anything added, it hardens because at room temperature, it is a hard solid. So your only way to speed hardening is to return the banana to the freezer for a short time. But then you are likely to get a condensation problem, so keep it as short as possible.
Best Answer
Since you specified not wanting any equipment other than a campfire and a stick, the best I can do is add one more piece of equipment you should be able to find anywhere (i.e., not have to carry with you): a rock.
If you put a flat-topped rock just to the edge of your campfire, you should be able to place a graham cracker and slab of chocolate on top of it. While you are toasting your marshmallow on the stick, the chocolate should start to melt. This technique won't produce totally melted chocolate (unless you have a very large, very hot fire), but the chocolate should get a little melty without being so runny that none of it makes it into your mouth.
This only works if you have thin Hershey bars or other chocolate in relatively thin pieces. Thick slabs won't soften all the way through with this type of indirect heat.
And for those people concerned about dirt, bring some aluminum foil to act as a buffer between the rock/dirty stuff and your s'more.
Extraneous but related note:
Your question got me thinking about ways to achieve melted chocolate with microwave s'mores (a last resort if I'm stuck inside with an electric oven or no oven at all), and I have an idea I'll test out tonight. When I microwave s'mores, I usually microwave the bottom graham cracker, chocolate and marshmallow together, then top with the other graham cracker once the marshmallow gets gooey. The chocolate doesn't really get melted that way, though, because marshmallows take almost no time at all to melt. I'm wondering if pushing the chocolate inside the marshmallow before I stick it in the microwave might help the chocolate melt more. I will update once I've had a chance to try this.
Edit: I didn't really notice any difference between microwaving the chocolate inside the marshmallow v. underneath the marshmallow.