How to add a line to the end of a file which I can access via sudo?

Depends on how much access your administrator has given you via sudo. The simplest answer, assuming that you have permission to do so, is to run "sudo -s" to get a privileged shell and then just do your

echo somestring >> test.txt

as 'normal'. If you need to do it automatedly:

sudo /bin/sh -c 'echo somestring >> test.txt'

The reason that what you have won't work (other than the fact that you left what I assume to be an "echo" command out) is that the file redirection happens in the context of your shell and the sudo only applies to the command you told it to run.

sudo bash -c "echo 'some string' >> test.txt"

The problem in your original try is that the ">>" is happening in the shell running as you; bash opens the file, not whatever is being run by sudo. In my version, you're passing the whole command including the redirection to a bash run by sudo.

% echo "string" | sudo tee -a test.txt

You can try ex-way:

sudo ex +'$put =\"some string\"' -cwq foo.txt

It's simple in-place file editing and it's useful in scripts, so you don't have to do any shell piping.

Lots of people recommend tee for this, but I don't like the side-effect of writing to stdout. An alternative is cat:

sh some_script.sh | sudo sh -c 'cat >> somefile.txt'

If cat had an argument like tee's -a flag, that would be a little handier:

sh some_script.sh | sudo pseudocat -a somefile.txt

But unfortunately it doesn't.