If the bill of sale for the bike is not from the last registered owner of record, this is a broken chain of ownership. DMV can't tell if the bike was stolen, taken without consent, or simply encountered incompetent but legal owners.
If you claim the title was lost and you only have a bill of sale from who you purchased it from, they can put it into the system as a new entry after a search of that VIN and the stolen vehicle listings in their system come back negative.
Think about it, if your bike is stolen along with the pink that you happened to have stored in the bike, and some years later is sold to someone else with a bill of sale from someone other than the legal owner of record, you would want DMV to accept this and give ownership to the newest "buyer"? There isn't even a chain of custody, let alone a continuous chain of legal owners in the eyes of the state. What is there to indicate that the seller on the bill of sale has any right to sell the property? All that does legally is show you had a good faith intent. If the vehicle is indeed on the stolen vehicle list, that BOS will get you out of criminal charges, but the vehicle will be impounded, and any money recovery will have to be through the court system via suing the illegal seller.
If the pink is unsigned, it is already technically an illegal transfer of ownership. Bring that to their attention, and you are asking for trouble, imo.
Many of the transfer laws were created to stem the trafficking of stolen vehicles. How is the current proposed transfer any different?
Might be that the value of the bike is so low, they will look the other way if in doubt. However, if you show them documentation that the legal owner has no representation in the current transfer, how is that NOT asking for trouble?
Best to plead stupid and hope DMV has not kept records of the bike's legal owner. Otherwise, a lien sale may be the only way to obtain title to the vehicle without owner of record written consent.
Legally, the deal looks shady to me. I would hope that DMV would take a similar view to keep criminal vehicle thievery suppressed. But, there is no requirement that DMV persons be competent, or have any diligence. But, I've certainly encountered some that did feel doing the job correctly was important.
Good luck!