If I understand you right, you want to make something like this:
http://pingmag.jp/2006/04/21/vectors-hektor-and-wobble-preventing-algorithms/
From what I understand, Hektor doesn't work with bitmaps, but rather vectors (hence its name, I think); the Arduino probably has enough memory to store a medium-complexity vector image.
If you are planning on painting a bitmap, though, you'll only be able to transmit so much data to the Arduino to have it paint; in fact, likely you'll still be transmitting position translation commands - the code on the PC controlling the Arduino would have to convert the bitmap into a series of "moves" to plot the image (it would probably be best to have it "random" fill the image, rather than top/bottom/left/right scan - it would just look more interesting).
Still, doing something like this, however you plan on doing it - won't be trivial, as already mentioned. But if you take it a step at a time, you can get there. As it has already been noted, start with getting a single motor turning (actually, I would start with the PC/Arduino communications portion - that always seems to be a hangup in projects of this sort). Work your way up from there...
