You can hide the recycle bin by changing the access rights in admin mode

1. click "set access rights"

2. select the recycle bin and select the groups that you want to still have access

3. check "Add selected rows and delete unselected rows" 

4. click save

Note that by default it is the group "Everyone" that controls what will be visible in the page tree structure in Edit mode. Removing read access rights for "Everyone" will hide the page in Edit mode for all but those specific groups that you give access rights, as mentioned. This can be applied to all page nodes in the page tree structure.