Yeah, you are missing a retaining clip. They cost about $2.30 from most auto stores. I'm sure you could ifnd them cheaper. I got my for free in the end.
They are small bits of plastic like you said. Round in shape with a raised triangle one side, and the square the other.
The triangle, which is inserted into the body is turned to lock. You then replace the bumper making sure you get the square side to seat in the mounting point on the bumper. To get it perfect, you'll have to remove the whole front bumper and slide them in, on both the left and the right. (which is not a huge job with only 6 bolts)
Generally these plastic clips are the first thing to pop-out or break if you rub somthing with your bumper.