Bash Script Permission Denied when tying to run
As we can see from the output of findmnt -T ., the filesystem on which the script is stored is mounted with the noexec option. This prevents scripts (as well as binary executables) from being executed directly, whereas bash bash_script1.sh still works because the bash executable is stored elsewhere and only needs to read the script.
To modify the behavior temporarily you can use the mount command:
sudo mount -o remount,exec /home
To make the change persistent, you will need to modify your /etc/fstab file and remove the noexec mount option for this block device.