How to access bash without a terminal emulator?

Yes, by pressing CtrlAltF2¹. That gives you access to virtual console TTY2 . And you can reinstall any terminal emulator from there with sudo apt-get install terminal-name, where terminal-name is, gnome-terminal for example.

To get back to the GUI, first type exit to log out of the virtual console, then press CtrlAltF7 to switch back to the GUI. (In case you want to keep TTY session open, skip the typing exit part)

Edit: June 17,2015

I've thought up another solution: if you have any C language IDE, you could compile the following code, and the console of the IDE will now give you access to bash

#include<stdio.h>
#include <unistd.h>

void main()
{
        system("bash");
}

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Note: CtrlAltF2 is not the only option. You can use CtrlAltF1, CtrlAltF3, CtrlAltF4, CtrlAltF5 and CtrlAltF6 too, which will give you virtual console TTY1, TTY3, TTY4, TTY5 or TTY6 respectively.

If you have an ssh server running, than you can connect via ssh from another system.

ssh <your_remote_user_name>@<your_remote_host>

If I install a system, then I first install and start the SSH server. A kind of life insurance. =)

Ctrl+Alt+(F1 through F4 at least, maybe up to F6) run a terminal interface on the virtual consoles. Once there, to get back to the GUI, use Ctrl+Alt+F7.

If you do any of those, you should be able to get to a terminal you can login to and then access the terminal. Bash scripts will, however, continue to run, if they're automated scripts dropped into cron and such or double clicked to run (but not in terminal). The terminal emulators which 'give you' an interactive shell, but ultimately bash, zsh, etc. which are the actual shells still exist and can run either via cron, scripts, and even the virtual consoles on the keyboard combos above.

Note though that if your scripts need the interactive interface, you'll have to use the virtual consoles, or install an emulator again.