sreten, I've wondered the same thing. As I understand it, your assumption is correct - air resistance is the only thing keeping a cyclist from going 100mph (if we had gearing to do so, of course). Bearing drag and rolling resistance are fairly minimal in comparison. There's no need to get into squared drag physics - the issue is simply the speed of the rider relative to the speed of the wind (assuming the wind is parallel to the rider).

I would think the same thing that you do: riding 10mph into a 20mph headwind should be roughly equivalent to riding 30mph on a windless day (assuming flat road in each case). However, as you note, riding 10mph into a 20mph headwind seems easier in experience. I don't have an answer for why this is. My best guess is that the actual headwind isn't consistent in terms of molecules - or as prathmann says, the effective wind speed is notably slower as you get closer to the ground, lowering the drag on the bike.