I've searched but haven't found anything talking about options for images for IYP products and their website doesn't seem to have much information at all...

Does anyone know if I can use an image with a transparent background to print an isolated image on a t-shirt?  Something like a bird?

Have you tried you upload a jpg with a transparent background?  When I make a file with a transparent background in photohop and save it as a jpg file, I get a white background.  I don't think you can.  You can save transparency in tiff but I don't know if they (IYP) support it.

For a transparent background, save as a transparent PNG file. (PNG-24)