Last month I returned from a 28-day Southeast Asia cruise, which involved multiple flights to get to Singapore and return from Hong Kong, as well as shore excursions in six countries. This meant lots of security screening. I just told the screeners I had a colostomy and pointed toward my pouch and said "I have a bag." On two flights I was taken to equipment where a wand was waved over my hands; other than that the screeners just let me pass.
Before I went on the trip I had output problems that just kept getting worse--continuous mush. Finally a friend suggested taking loperamide (Imodium) tablets. I googled "colostomy loperamide" and found that someone on the MeetAnOstoMate forum had been taking Imodium tablets daily for years without any problem. So I told my doctor I was going to experiment with dosage to find what works for me. I did and found one tablet with breakfast and one tablet with supper did the trick. Thanks to the tablets--which I buy on Amazon--I was able to travel without any worry about leakage.
(I also have to self-cath, i.e., use a catheter to pee. For the trip I took along a bag full of compact catheters and became very adept at using them quickly in a variety of public restrooms.)