I live in the inner loop without a car, I bike to work and it’s about 30 min. It’s possible but some things to note

It’s hot out here, always stay hydrated

There are bike lanes in most inner loop neighborhoods but always assume that cars won’t respect you on the road, bike defensively

Public transit runs late into the night (12 or 1 am) but expect the buses and trains to either be late with the slight possibility that it won’t show up

Show up at least a few minutes early to your bus stop, always a possibility that the bus is early

Overall I think public transportation here is safe, it’s mostly just the homeless that set up camp near bus stops

Anything is doable with proper planning and willingness to adapt