Must be the season - second time I've written this in a week...

Okay, so here's the deal.

Exercise in general is good at keeping you regular. But, there are a few things related to cycling that can cause issues.

First, you probably should push big gears (hard effort, slow cadence) while you're having an outbreak. Second, if the hemorrhoids are prolapsed (ie protruding), you will want to reduce them so they don't rub too much. You can do this by gently pushing them back inside while they're lubed.
Finally, getting dehydrated is really bad for the condition. You want lots of water during your ride.

Fruit is very good. Whole grains are very good - they have lots of soluble fiber in them *but* you have to take in enough water when you have them. If you eat a high fiber cereal, the milk doesn't have enough liquid, and you can make things worse. I hae a glass of water right when I get up, a big bowl of high-fiber cereal, then another glass of water.

Note that there is also a delayed effect. If you strain too much, it will cause you problems a few days later.

Some people find relief with steroid-based cremes. I think there's an over-the-counter version that has hydrocortisone, and there are also prescription cremes (cutivate is a good one). These are good but long-term use of steroids has some issues.

Stool softeners (dulcolax) can also make you more comfortable.

There's lots of good info on the various treatments online. Some are simple, some are more... invasive. Note that most narcotics cause constipation, which is a bit of an issue if you need them for the pain.

Finally, you might end up with a fissure, which is really really painful. A good treatment that works for many people is 0.2% nitroglycerin, which relaxes the muscles and allows you to heal. Some people get headaches during.