They key to both is to get them off ASAP. For bugs, I'd be careful about using any of those mesh covered sponges (especially with a darker color). I have one but only use it lightly on the bumper in worst case. Others have noted using Goo Gone or similiar products for bad cases.

As for the bird dropping, I carry an emergency kit (detail spray and two towels) to get it off before it dries. If it is dry make sure to resaturate it prior to trying to remove it. If acid etching occurs, try some paint cleaner or fine polish and then rewax. Alee from this forum has his own special techniques, so if yourun in to a major problem you may want to ask him