I'm not sure what type of ostomy you have. I have an ileostomy, and when I shower without the bag on I just let any output go down the drain. I do have a hand shower attachment to kind of "chase" any effluent.

My method is to have a little table next to the shower with paper towels (I use viva paper towels for my changes). I'll step into the shower, remove the old appliance and place it in a disposal bag on the table. Then I'll shower and when I am ready to get out, take a paper towel and cover the ostomy with it to catch any output. I'll then proceed to the counter where I have my ostomy supplies ready for my change and put a fresh appliance on.

Hope this helps.