Take your rubbish with you even if there is a bin.
As I am in a large motorhome I have the potential to be carrying more rubbish generating packages than a walker, and if I fill the bin the next visitor may not be as tidy. I brought it in, so I carry it out.
Also, if it is not beneath you, police the area before you leave and tidy away any other rubbish even if it is not yours! Simply put I am in a large, noticeable vehicle. Even if I have not dropped litter it is likely that someone will have seen me and may well lay the blame at my door.
The bins have to be emptied by someone and that's if the local wildlife do not distribute your rubbish around the bin.
When travelling to a new spot have a fall-back option in mind in case you find the place full, closed or whatever. Apart from the times when it is actually needed knowing that you have an alternative takes a bit of pressure off the end of the day.