This phrase is signed as "I RIDE BUSARRIVECLASS". This sign for BUS is more English-based, but is used often. Another way to sign BUS is the lexicalized version #BUS. You can see an example of #BUS in the conversation in ASL 1 - Unit 5.
This phrase uses a classifier and is signed as "ICL:1(me)"go" CL:1(me)"come back"". Christine uses the 1-handshape to show herself leaving and then returning.
I'm studying to be an interpreter.
This phrase is signed as a rhetorical question: "ISTUDYWHY? BECOMEINTERPRETER". The first part of the phrase uses the yes/no facial expression (eyebrows up) and the second part uses an affirmative facial expression.
I'm taking ASL classes.
This phrase is signed as "ITAKE-up ASL CLASS". This sign for TAKE is different from the sign you would use to indicate that you took (or got) something (i.e. TAKE-from).