This problem is common when trying to run Apache Tomcat on *NIX systems, like OS X or Linux.
This has in fact nothing to do with the BASEDIR environment variable, but really because you haven’t set execute permissions on all scripts in the tomcat/bin directory.
To do this, execute the following in a bash terminal:
chmod +x path-to-tomcat/bin/*.sh
If this fails because of permission issues, try the following:
sudo chmod +x path-to-tomcat/bin/*.sh
Remember to change path-to-tomcat to your own path.