F class is not Bench rest. Some clubs may hold informal matches and let you shoot from a bench, but F class is shot prone, from a bipod (F/TR class) and from a rest (F/O class). While some call it "belly benchrest", it is a competition governed by NRA rules. Real benchrest competitions are governed by IBS or NBRSA rules and are shot from a bench with pedestal type rest and sand bags.
F class matches are shot strickly for score, while long range bench rest matches are shot for score and group size. While F class can be very challenging, the scoring ring on the targets are larger than what they are on an IBS long range target. I would imagine this is due to the shooting protocal is different.
Back to the original question: bipods are not legal for IBS or NBRSA competitions.