To reach a value that is comparable to buying a high-end motorcycle like a Ducati V4, which can cost upwards of $20,000 to $30,000 or more, a Bicentennial quarter would have to be exceptionally rare. Here are three scenarios where a Bicentennial quarter might achieve such high value:
Proof coins from the San Francisco mint (S mint mark) were made for collectors and have a mirror-like finish. Although not rare in the general sense, proof or special mint sets in perfect (PF70 or MS70) condition can fetch higher prices.
Certain errors or varieties on Bicentennial quarters, such as double dies, off-center strikes, or misprints, can significantly increase their value. The more dramatic and rare the error, the higher the potential value. Nonetheless, it's exceedingly rare for these to approach the cost of a luxury motorcycle.
Some Bicentennial quarters were struck in 40% silver and were sold in collector sets. These silver coins are more valuable than their copper-nickel counterparts but still, under normal circumstances, do not approach the value of a Ducati V4.
For a Bicentennial quarter to be worth nearly the price of a Ducati V4, it would likely need to be a unique or extremely rare error coin that has significant historical, numismatic, or collector interest. Such instances are exceptionally rare and often involve significant auction competition to reach their high valuation.