Using some mulitiphonic based fingerings, you can play to an F (or even E) below the lowest B-flat on the bassoon. Here’s a demonstration:

The fingerings are basically normal notes with a node left open.

Low A: play low F but leave off the third finger of left hand.
Low G#: Play low E but leave off third finger left hand
Low G: Play low Eb but leave off first finger right hand
Low F#: Play low D but leave off first finger right hand
Low F: Play low Db. Slide the second finger of the right hand so that is only pressing the ring key alone, but not actually covering the tone hole.

On notes where it is possible and doesn’t disturb the basic fingering, you can add either the low B-flat key, pinky C-sharp or pinky D-sharp (i.e. low D-flat and E-flat keys) to stabilize the fundamental on some of these pitches. I’ve found them to be quite variable on different makes and models of bassoon, so you might have to experiment a bit to find stable fingerings for your setup. A solid reed that isn’t too soft is also really helpful.