It depends on how loong I am staying in the hotel. Many hotels dont have daily housekeeping, but you can request that they pick up the trash daily. If you feel like it or find it easier to explain why, just do it. I have never experienced or read about anyone having a issue by hotel staff when it comes to covering your needs. What ever they are.
I always wrap them in small plastic bags used to pick up dog poop. This conseals everything and makes me feel more relaxed about someone else taking it away.
If I request daily trash pickup I also put 3-4 bags in a bigger grocery store plastic bag and tight it up. Then I leave everything at the bathroom floor by the bathroom trashcan.
If I dont request daily trash pickup because I'm i.e just staying for 2-3 days.
Then I usually spread out where I put them.
1 goes in the plastic trashbag on the housekeeping wagon while passing by when they are cleaning other rooms.
1 goes in the gas station/shopping center/ wallmart/what ever outside trashcan.
1 goes in the next gas station/shopping center/ wallmart/what ever outside trashcan.
1 goes in what ever other location I can find. (Depending if I have a rental car) If there is a large dumpster available nearby, then this is heaven
I also do some Google streetview reseach on where available trashcans are.
On the last day before check out I put 3-4 bags in a grocery store plastic bag and leave it in the bathroom.