No, it isn't. Here's the Unix spec (http://www.opengroup.org/onlinepubs/007908799/), search it for bash and you won't get anything. That's a Linuxism (http://www.google.com/#q=linuxism), but it's not even on every kind of Linux.
The only standard shell on Unix is the bourne shell, and having things break because someone ignorantly hardcoded bash without using any bash-specific extensions is really annoying.
I agree it's worth the time to find a shell you like and customize it, but that's not a good reason to pick bash.