If I can't legally ride a motorcycle in my state due to licensing restrictions, what are my options for still buying one at auction?

You can still purchase and own a motorcycle without a motorcycle endorsement on your license — the restriction is on riding it on public roads, not on ownership or transport. Most buyers in this situation arrange transport to move the bike, then either get licensed before riding it, store it, or resell it. Check your state's specific licensing requirements, since some allow limited operation (such as in a parking lot) without a full endorsement.