I have added the following lines:

into .bash_profile and works fine but I would prefer to have a script that I would call run whenever I need to temporarily add "/new/path" into $PATH. So I tried using the above two lines but the change made to $PATH is visible only by the script itself.

You need to "source" the script to have the change exist after the script has been run. So if your script was called "test.sh" and you type "./test.sh", the change won't exist after the script has been run, it was executed in a new shell which doesn't exist after the script completes. But if you "source" it like this: "source test.sh" the change will persist as it will be run in the current shell, not a sub-shell, so any command run after that from that shell will have the desired $PATH. You can also source a file like this: ". source.sh".
HTH.
-G.

Unfortunately this doesn't work for me as I get an "ELF: command not found" error. I just tried to type the following:
and it works but then I have to type exit twice to logoff instead of once so it would be nice to have "source" work.

Not sure why you are trying the "bash --init-file", just try this:
that's just a period followed by a space, then the name of the shell script, and it should work. HTH...

As I said in my previous post, this doesn't work as I get an "ELF: command not found" error.

try out this

make an entry into your $HOME/.bash_profile

addToPath()
{
PATH=$PATH:/new/path;
export PATH;
}

that's it done! Now whenever you want to append path to your current path just write this on shell prompt.
$ addToPath

how do you add an entry to ./bash_profile ??

Just as you would with any text file---with a text editor.

Depending on permissions, you may need to open the file as root to be able to change it. In Gnome, sudo gedit <filename> (or just su, then gedit)