There's a subtle hack that you may be able to tweak to your needs.
First and foremost, realize that the 'trace' effect uses the text color for the trace lines for each character - a red character will have a red trace line, a blue character will have blue. It's possible to color each character differently, and it will have a corresponding trace line in the same color.
Then, there's an additional 'outline' trace that's used around the full text - this is drawn in the color of the bullet itself.
So the first option is you can create the text in, say, black *using a leading space character*.
Apply the Trace effect, then change the color of the characters *except for the leading space* to something different (e.g. red)
Now when you build, you'll have a black outline trace (because that's the first/bullet color), and the rest will be in the different color.
There's a second hack if that isn't good enough for you, which will take a little more work, but if you want your text to be red, for example, but you want your trace to be blue, overlay TWO text objects - one red, one blue.
Apply the Trace effect to the Blue text, and apply a different effect (fade, dissolve, etc.) to the red.
As long as the Red text object is 'above' the blue, you should see the blue trace lines coming in, with the red text overlaying.
You may need to fiddle with the timing to get it to look just right, but I think those are your options.