In my experience, some of the bikes that do best are ones that were never really rare... Schwinns were best-sellers BITD, and they've held their value very well. And, some of the most expensive Schwinns today tend to be models that sold very well.
Expense is, in part, a function of demand. (As mentioned above.) Many ppl want an old Schwinn b/c they once had one, so now they're nostalgic. Or, at the very least, they've heard of Schwinns and know they're collectible. so, demand is up, which brings the cost up.
The flip side is "supply", where rarity can add to the value. If something is both rare and in demand, it will bring a high price. (eg, Elgin Bluebird).
But, being rare doesn't make something valuable without that demand piece. There are many one-of-a-kind bikes out there that won't bring much money, b/c they're too obscure to be popularly sought-after. If you've never heard of it, how would you know to look for it? And, if you happen to find it, how will you determine a fair value if there are no others to compare it to?
FWIW, truly valuable collector's pieces tend to have a lot of info available about them online, with few examples being offered for-sale.