When I open a file in Sublime Text 3, at the bottom I have an option to set the Character Encoding as shown in the screenshot.
I can't set "UTF-8 with BOM" in the corner button either, but I can change it from the menu bar.
"File"->"Save with encoding"->"UTF-8 with BOM"
Into Preferences > Settings - Users
File : Preferences.sublime-settings
Write this :
"show_encoding" : true,
It's explain on the release note date 17 December 2013. Build 3059. Official site Sublime Text 3
Into the Preferences > Setting - Default
You will have the next by default:
// Display file encoding in the status bar
"show_encoding": false
You could change it or like cdesmetz said set your user settings.
By default, Sublime Text set 'UTF8 without BOM', but that wasn't specified.
The only specicified things is 'UTF8 with BOM'.
Hope this help :)