No reason not to use carbon or glass in bedding, as the resin doesnt have a lot of strength on its own. If you planned out your work, you could either go with chopped glass, or with cut cloth and tack it in place with some 3M77, wet it out, and so on.
Carbon is getting expensive these days since Airbus and Boeing seem intent on buying it all up. I'm heavy into the r/c slope soaring sailplane scene, and we've felt the pinch. Many guys who build ther own planes and can't afford carbon have gone to S-glass since its strong and reasonably priced.
If youre on the West Coast "Tap Plastics" is a great resource for entry-level composites. They also mail order if you dont have something nearby. ACP Composites also has it all.