In an Ember CLI app. If one wanted to use https://github.com/twbs/bootstrap/blob/master/js/tooltip.js
http://www.ember-cli.com/ does not seem to mention anything specific about this.
Where would this file typically be stored? At first glance, I was thinking of putting it in public/assets/js. What is the convention, if any?
Yes there is a convention. Use bower if a package exists. If it doesn't, download the repo into the vendor folder. Import the file in your Brocfile.js
app.import('vendor/path_to/main_js_file.js');