We did iron-ons, but I don't know if it would work with a picture. If you had a really good printer, it should. I would say buy the iron-on paper and a bag or even a t-shirt to experiment with. We used Wilton Easyimage transfer paper and it worked great! Just remember to mirror the image before printing Our bags were $5 a piece, but they are heavy canvas big beach bags... the transfer paper is about $1 per sheet, so it would certainly be cheaper if it works. Let us know how it goes!
Oh and as for if the iron-on is shiny, if you take the backing off while it is still hot, it gives a matte look. If you wait until they cool, they stay shiny.