I'm a 5 ft 10in male and here is how I handle my bag:
I wear an Nu-Way support belt nearly 24/7 due to a hernia that cannot be repaired. The good this does for me is it keeps my looking trim and fit at the waistline! :) I'm only 177 pounds so its not a huge issue to begine with but at age 55 there is a bit of muffin top. Its life.
Next I wear an Ostomoy Secrets wrap. This has a pouch for the bag ot fit into and holds it secure against my body. I've come to find this combo reasonably comfortable, but way better than not using one or the other.
I also wear an Ostomy Armor support/protection belt at times(with the Ostomy Secrets wrap. It works great for protecting my stoma when I participate in my main hobby, racing cars.
I tried the clip on plastic belt and found it just sucked, frankly.
I too have found as others have said the only person that notices your buldging pouch is you. I wear t-shirts, shorts, jeans, dress slacks, button downs tucked in, you name it no problems.
Here is a tip: You can turn your bag 90 degrees so it "hangs" horizontal, then use a wrap designed for that kind of wearing the bag. I am sorry I can't recall the name of the company that manes those wrap for that bag wearing method. It seems to work for active people as well. I do not use this method as doing so places the bag partly in the way of the seat and seat belts in my race car!
Hope this is of help, good luck and get out there!