FYI, I have a PR open to turn JavaScript Next into a tmbundle natively.
In case wanna try it:

Btw, I found myself unsatisfied by JavaScript Next, so I made my own bundle

that supports all the Babel features (ES6, 7, JSX). Basically I've just converted

the https://github.com/gandm/language-babel package to a TM bundle and

removed unneeded captured spaces in the regex rules.

I've been using it for the last month or so with no issues so far.

https://github.com/Igor10k/JavaScript-Babel.tmbundle