A pdf "Bill Monroe Songbook" can be downloaded (400 KB) at Monroe Songbook.

This is NOT limited to songs Bill wrote, but would give you about 200 songs he performed as a starting place. Unfortunately, it's lyrics only.

The book appeared several years ago, and I downloaded it then, but the site subsequently disappeared. On a wild chance, I searched for the "publisher" shown in my download, and found them at the above site. The book offered is the same "April 2000 edition" I already had. Google says they're located in Nashville, but several clues suggest the "group" - or whatever it is - has a Japanese tie-in. The new site seems to have a lot more up than when I visited previously, but I haven't poked around in it.

John