Learn English – “He broke out in a grin”

Indeed you can use it that way, although it's rare.

https://books.google.com/ngrams/graph?content=out+of+honesty%2Cout+of+courtesy&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Cout%20of%20honesty%3B%2Cc0%3B.t1%3B%2Cout%20of%20courtesy%3B%2Cc0

For example,

"...pay your tithes and offerings out of honesty and integrity because they are God's rightful due."

• Jeffrey R Holland

"I was too scared to tell Dada that I had confessed less out of honesty than out of the fear of being found out."

• Narendra Jadhav, "Untouchables: My Family's Triumphant Journey Out of the Caste System in Modern India"

You can also use "out of pity", as in the folk song, "Take Her Out of Pity"

https://www.youtube.com/watch?v=AiQrqnnCggg

"Come a landsman, a pinsman, a tinker, a tailor,

A doctor, a lawyer, a soldier, a sailor,

A rich man, a poor man, a fool or a witty,

Don't let her die an old maid, but take her out of pity,"

According to the Cambridge Dictionary

bubble

a situation in which you only experience things that you expect or find easy to deal with, for example opinions you agree with, or people who are similar to you

In the previous paragraph of the referred article such bubble is described

many of these routes take us to more of the same thing, or the same shade of different. The politics and the aesthetic tend to fall within a narrow — and comfortable — part of the preference spectrum.

Breaking out of the bubble is obtaining podcasts' suggestions from outside your circle (friends in Facebook, people you follow in Twitter, blogs you usually read, ...)

Notice that bubble is not a synonym for any problem. It's a specific situation whose details are explained in the dictionary entry. Breaking out the bubble does not mean solving any problem that you may face, that situation may not be even a problem for you. I've described what that expression means in your context.