Hi there Scotophor,
It was good of you to bring up these two interesting ideas. Yes, the ready made bicolor LED is an option. We havent talked about the series capacitor yet because i assumed that the readers here so far did not want to go through that trouble. It's a good idea however.
First, the bicolor LED with two LEDs in antiparallel.
I have one of these somewhere from long ago, but i can tell you that with this thing you would not want to use it as an indicator. It's red and green, and when the colors are both displayed (AC) it looks like, well, a dead fish
Crummy amber color, nothing like the nice bright yellow we can get today.
Also, it is not high brightness meaning we would have to use a lower series resistor or move to the series capacitor idea you mentioned. It's doable i think but i dont like the color of this type. Perhaps a more modern version if they make one with better colors.
For a better example of nice colors see the tri color LEDs. These things have beautiful color, at least for the three pure colors. Some colors mixes look nice, some dont. They would be harder to drive though because they have common anode or cathode to all three LEDs. So no back to back connection (anti parallel again) possible there, too bad.
The series capacitor idea is a good one if you dont mind going through the extra trouble of using the right kind of cap and building in some circuit protection against the cap shorting out on failure. A small bridge rectifier and it should work nice.
I actually built a couple of these just to see how well it would work. I can get the full 20ma that way. Right now i dont need that much brightness so i dont use them, but i could see how someone would want to use them for various things.
I was sure to add a surge protection resistor and zener and fuse too, things that make it safer to operate. I used to have a full blown schematic on my web site until AOL decided to kill AOL Home.