Not really, the bilateral are a package and the EU doesn't want CH to pick and chose.
If freedom of movement stops, a whole lot of thing also stop. It happened the last time SVP got something similar voted on (introduction of quota for foreign immigration), on a smaller scale (erasmus and horizon which are the higher ed and academic research collaboration, CH was a heavy recipient of the latter).
It really depends who is in power where when and if the 10mm limit is crossed. If there is a conservative in Paris or Berlin, chances are Switzerland can simply abrogate Schengen.
Of course if you have EU dismantlers in power anyway in FR/DE, they'll just be happy to sabotage.
I think we do bilaterally with our trading partners/border friends.
Freedom of movement across the EU has created a massive backlash. Politicians can keep ignoring that. Or they can modify Schengen, perhaps by admitting that FOM makes immigration decisions a collective one. (Germany letting in a massive wave of immigration means a massive wave of immigrants for everyone.)