There’s a lot of misinformation about the Wilderness Act of 1964 out there. It’s understandable because the law is complicated. In fact the Wilderness Act of 1964 has been amended only once since its inception, and the amendment had nothing to do with bicycle access to federal Wilderness. Properly read, the Wilderness Act does not forbid mountain biking in Wilderness, although various federal agencies have misread it and think it does, so they’ve written regulations that prohibit it.
Please see my law review article, published in the Penn State Environmental Law Review in 2004. It explains the issue. Any intelligent person can read it; you don’t have to be a lawyer to understand it. Here’s a link: