How do I use su to execute the rest of the bash script as that user?

Much simpler: use sudo to run a shell and use a heredoc to feed it commands.

#!/usr/bin/env bash
whoami
sudo -i -u someuser bash << EOF
echo "In"
whoami
EOF
echo "Out"
whoami

(answer originally on SuperUser)

You need to execute all the different-user commands as their own script. If it's just one, or a few commands, then inline should work. If it's lots of commands then it's probably best to move them to their own file.

su -c "cd /home/$USERNAME/$PROJECT ; svn update" -m "$USERNAME" 

The trick is to use "sudo" command instead of "su"

You may need to add this

username1 ALL=(username2) NOPASSWD: /path/to/svn

to your /etc/sudoers file

and change your script to:

sudo -u username2 -H sh -c "cd /home/$USERNAME/$PROJECT; svn update" 

Where username2 is the user you want to run the SVN command as and username1 is the user running the script.

If you need multiple users to run this script, use a %groupname instead of the username1