I'm in hotels about 75% of the year for work. I've never had any issues with leaving a used disposable in the trash can. Make sure the can has a liner. Before I leave for work, I'll tie the liner closed so the staff doesn't have to come in contact with the disposable. Don't leave a stinky diaper in the room, that'd just be too gross.
As others have said, take care of the housekeeping staff and they will take care of you.
I'm going to assume ALL hotels are equipped to handle bed wetters of all age ranges. Mattresses are expensive. If you are certain you are going to leak, then you should request a protective sheet from the front desk. If you destroy their mattress, you will be charged. Have fun with that expense report.