I have a Thinkpad W520 and have messed around with this extensively. I am not sure how much the W520 and T420S have in common, but I have written a blog post here outlining the big picture situation and giving some suggestions.
You should be able to get 2 hours of battery life using the nvidia card with proprietary drivers full time. That will also probably be the option that involves the least hassle when adding an external display (The program "disper" is very helpful for this). If the nvidia proprietary drivers for the card in the T420s function the same as for the W520, they will automatically underclock the card when it is not in full use (they call this "Power Mizer"), so your battery life will not be too horrible. Honestly, I only get a 25 or 30% increase in battery life by turning off the nvidia card. Also, I believe that with Bumblebee installed, you may not be able to use your external monitor because the nvidia card is already running an X server "under the hood". In summary, I would recommend pursuing option (2) further. Hopefully, once you get the proprietary drivers installed and working, X will autodetect everything and you will not have to mess with your xorg.conf.
When I installed and uninstalled Bumblebee, I had a little bit of trouble getting the nvidia proprietary drivers to work again. Here a few things to look into: (a) The W520 has BIOS options related to which graphics scheme is in use. I'm not sure what the T420 options are, but if you want to use the nvidia graphics on your Thinkpad display, you probably have to be in "discrete" mode. (b) You may have to mess around with the "jockey" program in ubuntu to get it to use the proprietary drivers.
Good luck! I hope this was of some help.
If you use nvidia-current-updates, you have to edit /etc/bumblebee/bumblebee.conf and set KernelDriver=nvidia-current-updates under [driver-nvidia].
It sounds that you've just installed Bumblebee, but that you've selected the universe repository during installation. That pulled in the nvidia driver which broke your 3D acceleration and other OpenGL capabilities. Try restarting the X server, e.g. by rebooting the machine.
In case the issue still persists, it is possible that some libraries have been installed in a wrong location. After installation of Bumblebee, /usr/lib/xorg/modules/extensions/ should not contain libglx.so, libglx.so.VERSION or nvidia_drv.so. If that is the case, remove those files (it requires root privileges):
sudo rm -f /usr/lib/xorg/modules/extensions/libglx.so* /usr/lib/xorg/modules/extensions/nvidia_drv.so
You may also have to reinstall the nvidia-current package if Bumblebee does not work afterwards:
sudo apt-get install --reinstall nvidia-current
Re-login and your problem should be solved.
Best Answer
The well named "initial support", is an initial support. Basically that means you could use full power of your optimus graphic card without no need of bumblebee/prime. But, you will soon notice that battery life will strongly decrease (In my case around 1h).
I would recommend you to keep bumblebee installed to keep a "normal" battery life.