Marion, I remember being a noodler myself (not that I don't still occasionally do it). One thing I recall about learning tunes this way is that you try to figure out which are the most important notes, maybe the ones that are accented, or seem to give the feeling to the tune. Then, once you got that, you can fill in the rest. As far as being unobtrusive, which probably is a good idea sometimes, for the fiddle you can buy a mute, a little rubber thing that you push down over the top of the bridge, strings and all. Should be easy to find in a music store that caters to string players. A cheaper and almost as good alternative is to stick a spring-type clothespin or maybe two on the bridge from the sides. Good luck and don't stop.

Chet