I shower with the bag on every day except when I'm changing it - then I shower totally naked :)
Try not to make ostomy care any harder than it should be. I can understand the plastic wrapping for now while your wound is still new but once it's healed, don't worry about
using it. I don't do anything special when showering. When I get out of the shower, I towel dry my bag (it has a thin cloth covering over it) and that's it. Some people like to use a hairdryer on it's lowest setting to dry the wafer but I never have time for that. Body heat does the job just as well, just takes a little longer.
On change days, I take the whole bag off, step in the shower and let the water run over Harriet (my stoma). She loves the warm water and it helps get her really clean. If she decides to spurt while I'm in the shower, it all just goes down the drain anyway so I never worry about
that one. I then hop out, put a tissue over her, towel dry around her and make sure she is really dry and then proceed to put an Eakin Seal and my one piece bag on.
You can shower with just the wafer on, but it's not really recommended cos the water can erode the wafer and reduce weartime. Having said that, it's personal preference so if you want to shower with it on, go for it!
Hope this helps.
I have had an ileostomy for 30 years now due to UC.