Eros... there's a few threads referring to "moon cups" or "diva cups".

My connection is too slow to find the links for you, but either do a search, or mebbe someone else can provide the links.

I used to ride using a tampon (or two on the really heavy day) but you need to be careful about string placement.

Pads just move about and disintergrate.

I find although I bleed more if I ride during my period (and consequently my period is up to 1 1/2 days shorter) my cramps are milder and discomfort is much less.