Installing OS from bash?

As a small learning project Id like to make myself a small system image/reflash utility that doesn't need livecds etc., with possibility of starting a reimage from Grub (I'm on Ubuntu by the way). For this to be possible I'm thinking I need to make a small partition that has enough system functionality to run bash, rsync, mount drives and possible more... Im thinking maybe Ubuntu core?

Question is - Can I install a distro by bash only? As in I make an install program for my small utility that partitions drive, sets up this minimal os and sets up rsnapshot/sync functionality and Grub entries.

If you think this is the wrong way to go about achieving this, your input would be appreciated as well :-)

Thank you

EDIT: thank you for the replies all. I wrote this right before Bedtime and I am on vacation with the family, so meaningful replies will take a while (when I have som downtime) but I will get back to you. Thank you