Printing on fabric with an inkjet printer may sound scary, but it's easy and fun. You can now purchase ready to print fabric sheets that you print just like paper.
Results including colorfastness will depend on the ink used in your printer and the brand of fabric sheets you choose to use. I would suggest trying a variety of brands at first to find the best match for what you want to do.
If you'd like more information on printing on fabric please visit the sites and YouTube videos below. I have not tried all of the products listed but did a google search for your convenience. You may find there are additional products and resources available beside what I have found for you here.
Dharma Trading
