The best possible outcome of a bourgeois democracy is that it fails so spectacularly at organising itself that workers are forced to organize as a result.

But that never happens because industrial capitalists are actually really good at organizing labor through exploitation that if they're allowed to continue to exist they'll subsume the failed state and institute feudalistic or fascist ideologies.

So yeah, we gotta liquidate the bourgeoisie either through proletarianization or other means if we ever want a spontaneously organized worker's democracy to form.