It's a mismatch. It's almost like asking, "What could an unarmed man do against a sabre?" (Run or get inside the point.) Granted, though, that with a large Bowie you are armed with what is essentially a small sword of sorts, it would be very difficult to a) parry the sabre's cuts and thrusts b) riposte to the hand of the sabre fighter - but it could be done.
In "Fighting with the Sabre and Cutlass" (Cold Steel), Lynn Thompson and Anthony DeLongis spar with sabre vs. cutlass and the cutlass man shows how it is possible to defend and attack with the shorter weapon (assuming both opponents are equally skilled) - although it is difficult given the reach advantage that the sabre man has. A cutlass has about twice the reach as a Bowie, so I think that the difficulty factor with the Bowie has to be much greater.
Best,
Steve Lamade