Can I get by without a car as a UW student in Seattle?

I will be a grad student. I've heard traffic is terrible in Seattle, and it seems like every apartment charges at least an extra $50 a month to park a car (which is unheard of where I'm from!). Ideally, I'd love to live in a city like NY with great public transportation. I will have free bus passes while I'm a student. Are the buses around UW fast and reliable? How far are major grocery stores from UW campus? The only issue is when I graduate, no longer have a free bus pass, and need to get to a job, which will most likely be downtown. Thoughts? P.S. my bf and I may share one car...I am just hesitant selling my own car.