DVD with both 32-bit and 64-bit Ubuntu

You can create a DVD that contains both versions of the live CD:

1. Download ubuntu-13.04-desktop-i386.iso and ubuntu-13.04-desktop-amd64.iso.

2. Create a folder structure for the DVD:

   $ mkdir -p ubuntu-13.04-desktop-i386-amd64/boot/{grub,iso}
   $ mv ubuntu-13.04-desktop-{i386,amd64}.iso ubuntu-13.04-desktop-i386-amd64/boot/iso/
   

3. Save the following as ubuntu-13.04-desktop-i386-amd64/boot/grub/grub.cfg:

   # Derived from /boot/grub/loopback.cfg from ubuntu-13.04-desktop-i386.iso and ubuntu-13.04-desktop-amd64.iso.
   
   menuentry "Try Ubuntu without installing (32-bit)" {
       loopback iso /boot/iso/ubuntu-13.04-desktop-i386.iso
       linux   (iso)/casper/vmlinuz  file=/cdrom/preseed/ubuntu.seed boot=casper iso-scan/filename=/boot/iso/ubuntu-13.04-desktop-i386.iso quiet splash --
       initrd  (iso)/casper/initrd.lz
   }
   menuentry "Try Ubuntu without installing (64-bit)" {
       set gfxpayload=keep
       loopback iso /boot/iso/ubuntu-13.04-desktop-amd64.iso
       linux   (iso)/casper/vmlinuz.efi  file=/cdrom/preseed/ubuntu.seed boot=casper iso-scan/filename=/boot/iso/ubuntu-13.04-desktop-amd64.iso quiet splash --
       initrd  (iso)/casper/initrd.lz
   }
   menuentry "Install Ubuntu (32-bit)" {
       loopback iso /boot/iso/ubuntu-13.04-desktop-i386.iso
       linux   (iso)/casper/vmlinuz  file=/cdrom/preseed/ubuntu.seed boot=casper only-ubiquity iso-scan/filename=/boot/iso/ubuntu-13.04-desktop-i386.iso quiet splash --
       initrd  (iso)/casper/initrd.lz
   }
   menuentry "Install Ubuntu (64-bit)" {
       loopback iso /boot/iso/ubuntu-13.04-desktop-amd64.iso
       linux   (iso)/casper/vmlinuz.efi  file=/cdrom/preseed/ubuntu.seed boot=casper only-ubiquity iso-scan/filename=/boot/iso/ubuntu-13.04-desktop-amd64.iso quiet splash --
       initrd  (iso)/casper/initrd.lz
   }
   menuentry "Check disc for defects (32-bit)" {
       loopback iso /boot/iso/ubuntu-13.04-desktop-i386.iso
       linux   (iso)/casper/vmlinuz  boot=casper integrity-check iso-scan/filename=/boot/iso/ubuntu-13.04-desktop-i386.iso quiet splash --
       initrd  (iso)/casper/initrd.lz
   }
   menuentry "Check disc for defects (64-bit)" {
       loopback iso /boot/iso/ubuntu-13.04-desktop-amd64.iso
       linux   (iso)/casper/vmlinuz.efi  boot=casper integrity-check iso-scan/filename=/boot/iso/ubuntu-13.04-desktop-amd64.iso quiet splash --
       initrd  (iso)/casper/initrd.lz
   }
   menuentry "Test memory" {
       loopback iso /boot/iso/ubuntu-13.04-desktop-i386.iso
       linux16 (iso)/install/mt86plus
   }
   

4. Generate an ISO image (You may need to install xorriso.):

   $ grub-mkrescue --output ubuntu-13.04-desktop-i386-amd64.iso ubuntu-13.04-desktop-i386-amd64
   

You can now burn ubuntu-13.04-desktop-i386-amd64.iso (1.6 GB) to a DVD and choose either 32-bit or 64-bit options at boot.

Note: This worked for me in a virtual machine. I strongly recommend testing it using one DVD before burning multiple copies.

To my knowledge, no there isn't. If you want to spare DVDs, you can use USB sticks (assuming you have one (or more than one) and your computer supports booting from USB stick).

In Ubuntu download page, there is step-by-step instructions for creating bootable Ubuntu USB sticks in Linux, Windows or Mac OS X.

There is no official 32/64 bit image available and I'd doubt if you would be able to compile one to do what you want.

The difference between 32 and 64 bit is hardware based so having two cd's or usb keys with 32bit and 64bit version of Ubuntu on them would be your best option.

If you only have access to one cd or usb create a 32 bit install - it will be usable on both types of architecture.