I've never done this, Twinkle, so I don't know. It sounds like a really cute idea! I used to have my first graders decorate a t-shirt with fabric paints and puffy paint. Some of the paints in the bottles that they wrote with (sorry -- I don't know what it's called) would crack and come off of the stretchy material after repeated washings and wearings. This was 15 years ago, though, and paint formulas may have changed since then.
You might want to check and make sure that won't happen on the terrycloth bibs. I'd hate to think of a baby chewing or sucking on the bibs and having the paint break off/be swallowed. Maybe a smooth fabric instead of terry, and permanent fabric pens?