Is it possible?

I've got 'testme.sh' as a text file, and it just has in it "path/to/my.app" (without quotes).

When I run it from within Terminal, it just says my.app is a folder. Which, I get why it's saying that, but I just want to run it, not browse it; is that possible to ddo within a shell script?

Yes - just use the path to the executable. For example: example.app/Contents/MacOS/example

If you mean to run it as if double-clicked from the Finder, you can use the open command. open path/to/my.app

Ah yeah, got it working now; many thanks guys.