My assumption was the bitter compounds would be flavenoids but it seems this is not true. I'd say bitterness isn't of itself material to IBS its an effect higher in the gut tract. Gall for instance is very bitter and acrid, but necessary for digestion.

What is material is that coffee has a lot of interesting components beside caffeine.

However, I believe my rapid fight/flight gut emptying impulse after a cup probably is the caffeine.

(I have disregulated gut, my gut man (who said the disposable sigmoidoscope revolutionised his speciality) said I was just shy of IBS)

You can test if it is caffeine for you by trying sodas, chocolate, teas, and even caffeine pills.

At least in my own anecdata of IBS, caffeine alone does not have a laxative-like effect for me. I have noticed some but not all strongly bitter foods do, and heard a theory once that some flavoring compound that tastes bitter may be subtly enough like gall passes through the stomach to confuse the gut into thinking there may be a gall leak and to flush the system faster. That certainly sounds right to my anecdata, but also part of why I think I crave bitter foods sometimes (as an IBS-C to IBS-D switch/trigger).