That's what I do. If it's bad enough, put the resident in the shower and rinse it all down the drain!
We don't have wipes at my facility but most of our toilets have sprayers. Those are much better than bagging everything up and bringing it to the hopper, which sprays so forcefully that you end up with a mist of dirty water in the air and dripping down into your gloves*. I just throw the soiled stuff in the toilet and stick the nozzle under water so there's no splashing and spray away.
*I wish they made opera-length gloves.