Oo, cheese on the Web! I like cheese! Here's one possibility.
Draw your swoosh with the Illustrator brush tool. For the sake of example, use the stock thick pencil brush. Object>Path>Add Anchor Points a few times.
Duplicate the swoosh for about as many times as you have points. Delete an increasing number of points from the right of each copy, so that you have your sequence. The texture of each line will look a little different as the brush pattern shrinks, that's desired.
Stuff each of your lines into its own layer, and overlay the segments. It's okay if they don't seem to line up perfectly, this will give you a spreading ink effect later on.
Export the mess to a PSD with layers and jump over to Photoshop. Change the layer types from pass through to normal, to appease imageready. For each layer, Layer->Smart Objects->Group into smart object, then finally rasterize all the layers, again all to make ImageReady a little less fussy.
Over in ImageReady, with the rest of your stuff dragged in, make as many frames as you have layers. In the first layer include only the shortest stroke, the first two layers in the second frame, and so on, so that they build up and look a little bleedy.