Vince,
I was talking about MobileWeb. It's an ugly hack, but it works. Download the Firebase script to your project, then edit it to add module.exports = Firebase; at the bottom then require it as a module. It works, but requires maintenance when new Firebase releases come out.
The bad news is that I developed a Titanium native iOS module some time ago, and it works-- mostly. The problem is that as Firebase usage increases, and the user interface complexity increases, especially on slower devices, Titanium's single-threaded Javascript environment intermittently hangs. The user interface is stuck, the debugger says nothing is happening, but setTimeout() calls are not made, in fact nothing on the Javascript stack gets called. Other iOS threads such as the Firebase module are all happily running and logging activity, but the Titanium JS thread is stuck. Only quitting and relaunching the app fixes it.
I haven't done enough testing to see if the same problem occurs in MobileWeb or Android.
To get my project finished, I'm in the process of replacing the worst offending Titanium window with a native iOS module, with no Titanium involvement other than loading the window. I'm really not impressed with Titanium's robustness, nor the Titanium developer community who were unable to offer any suggestions on how to track down the hang.
My advice to newcomers is: don't mix heavy Titanium user interface with heavy Firebase data interaction.
Regards
Thomas