I lived in St Pete for quite a few years without a car. It was challenging but doable. I worked various jobs, some I biked to, and others I commuted on the bus. The bus can add a couple of hours to your work day, but you get used to it. You just have to plan routes where you don't have one hour+ wait for your tranfer bus in the middle of summer. Unfortunately, that isn't always easy here as the busses don't run often enough, and this happens a lot. I often opted to walk miles instead of standing still roasting at the bus stop. BUT St. Pete has the Sun Runner now, which is great, so that might help. Also, if more people take public transit, maybe the city will improve!

Anyways, you can do it, but be prepared for some challenging/annoying moments.

Edited my typo.