I suggest you do a search in this forum with the keyword "commando", you'll find LOTS of discussion on this hot topic.

I can't imagine wearing panties under my bike shorts, but as Nanci's experience shows, you don't die from it (although you can get looks from other cyclists). I do suggest that you try to find a pair that suits your preferences and try it a couple times, without panties. If you can't do it, just keep the panties, but make sure you find a type that doesn't chafe (like Nanci did).

I also prefer thicker lycra, but I'm not sure if this has anything to do with your question...

Besides, I understand how you can be self-conscious, but that's mostly what it is: self-consciousness. Most of the people that look at you will not "see" your bike shorts, your panty-lines or absence thereof, etc. They just see a cyclist. So don't sweat it too much.

Keep riding!