Can you measure the width of a character in an AE expression?
So you want the width of the whole text object no single characters?
In that case you could use this: http://motionboutique.com/text-bounds-expresssion-580/
A tutorial plus sample project on how to get the bounding box of a text layer.

In case the link dies, here is the complete expression they use to determine the bounding box.

step = 1.0; // higher values speed things up (2 means two times faster) but reduce precision
L = thisComp.layer("MyTextLayer"); // text layer whose size must be evaluated

w = thisComp.width;
h = thisComp.height;
halfW = w / 2;
halfH = h / 2;
halfStep = step / 2;

left = w;
right = 0;
top = h;
bottom = 0;

// find left
found = false;
for (x = 0; !found &amp;&amp; x &lt; w; x+=step)
{
    if (L.sampleImage([x,halfH], [halfStep,halfH], true)[3] &gt; 0)
    {
        found = true;
        if (x &lt; left) 
            left = x;
    }
}
// find right
found = false;
for (x = w; !found &amp;&amp; x &gt;= 0; x-=step)
{
    if (L.sampleImage([x,halfH], [halfStep,halfH], true)[3] &gt; 0)
    {
        found = true;
        if (x &gt; right) 
            right = x;
    }
}
// find top
found = false;
for (y = 0; !found &amp;&amp; y &lt; h; y+=step)
{
    if (L.sampleImage([halfW,y], [halfW,halfStep], true)[3] &gt; 0)
    {
        found = true;
        if (y &lt; top) 
            top = y;
    }
}
// find bottom
found = false;
for (y = h; !found &amp;&amp; y &gt;= 0; y-=step)
{
    if (L.sampleImage([halfW,y], [halfW,halfStep], true)[3] &gt; 0)
    {
        found = true;
        if (y &gt; bottom) 
            bottom = y;
    }
}

/*"Size of text\n" + (right-left) + "x" + (bottom-top)*/
left + "," + top + "," + (right-left) + "," + (bottom-top)