All good questions.
First, there is danger in assuming that it is IBD or cancer, although that is probably what is there.
I would assume since you think your cat has inflammatory bowel disease that your cat has already had full blood panel including thyroid, fecal test for parasites, hypoallergenic food trial, folate/cobalamine levels, specific feline pancreatic lipase test, abdominal ultrasound, and a biopsy of the intestine by either exploratory surgery or endoscope? IBD is a very expensive diagnosis. BUT, if you haven't done all of those things it is just guess work. And, honestly, even when you get to the end of that diagnostic work up the results are often inconclusive as well. This is why IBD is so darn hard to treat.
I understand though if you don't have the money for the biopsy and all the tests. Usually it is kind of disappointing even if you do because the end diagnosis is often "either lymphoma (cancer) or IBD" even after all the tests. So, sometimes treating is guess work, and sometimes, that's ok. BUT, because we don't have a definitive diagnosis, you won't be able to say if the medications should be working, have worked, or whatever.
Sometimes with IBD you get flareups that go away on their own inspite of the tylosin or prednisone/prednisolone. That makes it real frustrating and difficult to know what you have used has or hasn't worked! *Sigh*
With that in mind, it is hard to treat. There is pain and discomfort for the pet mostly caused by infilltrative disease in the bowel. This inflammation is similar to certain cancers like intestinal lymphoma so much to the point that it is hard for even trained patholgists to know the difference when doing histopathology on the tissues. But, the inflammation is usually cellular in nature, and often infiltrative meaning the white blood cells are invading into the intesinal wall, lymph nodes, etc and causing the painful inflammation.
Often one of the best medications is prednisone for controlling the inflammation. This has the extra benefit in some cats of increasing the appetite and relieving the pain and discomfort. If you haven't tried canned food (Friskies works best I think - although I don't love that food - it's just cats do) try it. BUT to answer one of your questions, yes, prednisone/-olone do often work VERY VERY fast. Even if it is cancer. The most common cancer is lymphoma in the intestine and that is usually small cell lymphoma. Prednisone was one of the first drugs developed for treating lymphoma in people back in the late 50's. It's still considered a chemotherapeutic drug today. So, you can see how it would treat IBD and cancer.
Problem is... it doesn't usually last forever. You do start to see signs returning when discontinued. Often this will be a lifelong drug. You could wean off over time when the signs are controlled. And I will typically wean down to the lowest effective dose. Often you will never wean down completely.
I will often continue the tylosin as well, life long. Which one was working and which one wasn't? Was the pred the one that is working and tylosin not? Truthfully, who knows. We just don't understand IBD and the treatment well enough to tell you that. If it is bothersome or worries you to give so many medications, you should know that this is the path with IBD. There is no other way.
Also discuss using budesonide with your Vet. This drug has been shown to be a little more effective at controlling flare ups of IBD in cats. In severe cases where that doesn't work chlorambucil has been used (especially when small cell lymphoma is a possibility).
She should still be able to go outside with you under supervision unless she is on 10 mg or higher of prednisone twice daily. Or roughly 1mg per pound or higher... I don't know how much she weighs.