My company has several suppliers that print and sell tee shirts in bulk. I can usually get them for around $3 - $5 per shirt depending on the materials and the size of your images. Feel free to email me at email@example.com and I can give you more specific product and pricing information.
It's kind of expensive to set up to do a job as specialized as this sounds. You'd need a screen, squeegee, inks, film, masking, and a design simple enough you could cut it yourself. It's a whole semester's worth.
You might have better results by designing your patch, either in the computer, or by hand, in pen and ink, or watercolors, or whatever, then taking it to Kinko's and having it made into an iron on transfer. They look great, and they'll probably last at least as long as the band.