I have issues with flying as well. As far as anxiety/panic attacks, I do have to take an anti-anxiety med before a flight and that helps a lot. I'm not sure you have meds for that, so I recommend that during the flight it helps to listen to your favorite music and try to keep your mind occupied by doing logic or word puzzles and reading magazines. Are you traveling alone?
What are your IBS symptoms? If you're an IBS-D (diarrhea), you might want to try taking half a dose of Imodium as a preventive -- then you won't have to worry about having an attack on the plane. It's not good to fast, because that will only aggravate your symptoms. As someone else suggested, try to eat small, safe, mainly soluble fiber meals throughout the day. Take some snacks with you on your trip -- Rice Chex, low-fat crackers -- and tea. You should be able to ask the flight attendant for hot water. Teas for IBS: peppermint, fennel, ginger. Teas for anxiety: chamomile, lavender.
I'm not sure if it's better to just get the flight over with or to do two shorter flights so you'll get a "break." I kind of think just one flight would be better because then you don't have double the anticipation of getting on two different flights.
I wish you the best of luck on your flight! You can do it!