The second sentence is perfect.
The first one needs either a definite or an indefinite article before bus both times the word appears. The definite article is more common when referring to modes of surface transportation: I like to take the bus when I'm in London. I took the ferry across the river. I took the train to Cambridge. For some reason, we don't usually use the definite article when talking about flying: I went to Chicago by plane. I took a plane to Chicago.
Student or Learner