Yes, i take bart every day from the city out to Hayward where i work. An yes, its a very comfy speedy ride! I used to have a car when i lived in Los angeles and in texas, but in cities like SF and New York you really dont need a car!
During rushhour the trains go every ten minutes, but after 8pm some lines stop going, like Fremont to Dala City so you have to transfer between Bay Fair and Lake Merrit! But thats the only "hassle" i ever had with it. Plus they have very comfortable upholstered seats! I would take the bart, but it totally depends on the nature of your visit to the hospital.