Make sure you are very well hydrated during that time. It will help a lot.

You know, I have nasty periods, but just before the Cinderella this year, my friend and I decided to do a 65 mile ride. Of course, my period started that morning. Let's just say the first two days of my period are incredibly heavy. We did the whole ride and I felt surprisingly good. I took Advil every so often, too. Ended up being the shortest period I've had since having kids. Amazing!

So maybe it won't be as bad as you think. I do use the Instead cups, which are disposable and last much longer than a tampon will. You can search the forum, as others suggested, to find out about alternate hygiene products.

Hope your ride goes great!