What is the meaning of "bail on his life and set up shop in someone else's.” in the first episode of Rick&Morty?

Solution 1:

In BrE,

bail is an idiom which means:

bail on (one)
‘To leave or abandon one’.

Source: https://idioms.thefreedictionary.com/bail+on+someone

The sentence he can’t just bail on his life means “he can’t just give up on or abandon his life”.

“He can’t just bail on his life and set up shop in someone else’s (life)...”

Set up shop is an idiom with different meanings and I shall quote the meaning referred to in this quote, it means “to occupy or takeover a space” in a basic sense:

(2) By extension, to establish oneself in a particular location for a prolonged period of time.

Examples:

When I was a freelancer, I used to set up shop in my local café everyday, usually in the same seat!

There are a few regulars who come in nearly every afternoon and set up shop at the bar until closing time.

Source: https://idioms.thefreedictionary.com/set+up+shop

Altogether, the meaning is quite figurative but the general sense is:

(He) can’t bail on his life [give up] and occupy/live in someone’s life

As @Kris said in the comments the latter, might mean he cannot give up on his own life and depend on someone else’s life.