I might be remembering this wrong but I seem to recall being able to start out on a bus in Livermore and make all the way to Fremont (or Frisco once to see The Smithereens doing a free concert in Justin Herman Plaza on a school day) just using transfers from the original ticket. Pretty sure the BART ticket would get you on a bus but not sure about the other way around as this was quite a long time ago.

Pretty good deal for a delinquent minor with hardly any money.