The Puppy Installer program does not install a boot loader needed to boot the Bionicpup32 install.
You have to do that separately using a boot loader install program.
With there being legacy bios and UEFI bios computers and how they boot.
What boot loader to use and how to set it up is a little confusing.
You still have the old grub boot loader that Ubuntu was using.
You have to manually put an entry in it to boot Bionicpup32 or install a new boot loader replacing the old grub one.
You can try to install the Grub4dos Boot loader.
Use Grub4dos bootloader config.
Select the SSD as device to install on.
Select search within only this device.
Use the default settings and change nothing else.
OK.
OK.
OK.
Done.
Now try to boot from the SSD.
May need to go into the computers bios and disable secure boot.
If all you want on the SSD is Bionicpup32.
I suggest you start over fresh.
I suggest you use the Frugalpup Installer program to do the install.
Boot Bionicpup32 from the USB install and do all this from it.
This is what I do.
Using Gparted program.
Delete all partitions on the SSD.
Setup the SSD with 2 partitions.
First one, small 300MB, fat32 format, flagged boot. (location for boot loader files, boot partition)
(this is UEFI standard requirement, and some computers, look for a fat32 partition, for boot loader files)
Rest of drive, whatever other partition(s), but one ext 3 or 4 format. (location to put frugal installs)
Ext 2 format is OK, but it can get corrupted easier.
Run Frugalpup Installer main program.
On the main window are selection buttons.
Select the Puppy button, to do the install.
Go through install process, selecting to install to the ext formatted partition on the SSD.
Note:
When selecting the partition to install to.
A window pops up, giving option to make a directory, to put the frugal install in.
I make this directory and usually name it, the name of the Puppy version.
Carefully read that windows info.
Press enter, makes the directory, not the OK button.
complete the install.
When it gets back to the main Frugalpup window.
Select the boot button.
Select the location of the frugal install, on the SSD.
Select the small 300MB partition on the SSD, as location to install the boot loader. (may need to scroll the selection window)
Select the boot loader type.
UEFI
mbr ->legacy bios boot
both
You can install the UEFI for UEFI computers, mbr for legacy bios computers, or both, to boot anything.
The UEFI will also install the needed files, to support secure boot enabled in UEFI.
When you first boot the SSD, on a UEFI computer, with secure boot enabled.
A process will start, to allow you to install the Puppy security key, to the computer.
It will add this Puppy key, to the other ones, loaded on the computer.
If you want to do another Puppy version frugal install to the SSD, so you have multiple Puppy frugal installs.
Do the complete Frugalpup Installer process again, for the new Puppy version.
When you run the boot loader install.
It will make entries, for all installs it finds, on the USB drive.