Yes, it can be done in ImageReady. You may need to familiarise yourself more with the program first, but I'll sum up what I know:
1/ Make your image in Photoshop. Set up a layer for your background stuff, then put each bubble on a separate layer. You'll need to know how to draw a bubble with transparency, however. If you don't, try finding a tutorial on it, perhaps from
http://www.good-tutorials.com.
2/ Send the document to ImageReady (there's a button on Photoshop that'll do this, find it).
3/ Open the Animation window if it's not (Window >> Animation). You'll see that you have just one frame. Hit the icon to the left of the garbage can to duplicate the frame.
4/ In this second frame, move all your bubbles to where you want them to end.
5/ Select all layers with bubbles, and select both frames. On the far right of the Animation window, there's a circle with an arrow. Click it, then go to Tween.
6/ Set these parameters:
Tween With: Selection
Frames to Add: (This is your own decision, you compromise filesize for smoothness. Experiment with this; if you don't like the results, hit Undo and do it again.)
Layers: All Layers
Parameters: Position
7/ This should add a bunch of frames. Hit Play on the Animation window to see what it looks like. At this point, all your bubbles will be travelling in straight lines. If you want them to curve, you'll have to repeat this whole process several times (ie. duplicating your last frame, then moving the bubbles somewhere else, then tweening). You may also try moving the bubbles manually in each frame.
I hope you can understand this...but you'll really need to get the hang of the programs in order to maximise effectiveness.