You can find out the exact route of the public transportation that is a block away here http://www.viainfo.net/BusService/Schedules.aspx - unless there is a direct route to where you want to go downtown, it will waste a ton of time. Outside of downtown or direct buses to downtown you should just drive. If you want to go to Austin, I would leave San Antonio by 5 AM or after 9 AM and don't try to return before about 7 PM.