In context, the speaker is comparing her former commute--walking to her own garage--to a new commute that requires one travel segment by rail and one by bus. I wish I knew more of the source for the speaker in the original article (which appears to be p. 8-9 of McMillan coursebook Ready for First) as this usage may be colored by her background and the nature of the transportation network in her region.
First, I disagree with the other answers claiming that "I take the train" is a reference to a specific train or train time. That just means the rail network. For instance, in NYC dialect, "the train" is the most native way to refer to the subway system. Prior to COVID-19, I would have described myself as "taking the train to work"--even though on a given day I might choose any of six or seven different trains running on three different lines, departing at three- to seven-minute intervals. (In NYC, the vast plurality, 40%, of commuters use the subway; taking the train is just a background assumption for daily life. I believe this is true in most US cities that have decent rail/metro systems.) You'll see this in broader/non-regional usage as well wherever bus systems are common: without further context, the expression "take the bus" refers to using the bus system generally, not to a particular bus line or departure time ("A: Should we drive to the game? B: Nah, I wanna have a few beers, let's just take the bus"). In fact, if I wanted to emphasize a departure time or a particular bus, I would probably say "my bus"--example: "Hurry up and get your shoes on, if we don't leave in the next five minutes I'll miss my bus."
So that leaves the question of why "the train" but "a bus." I read "a bus" as emphasizing an unusual extra burden of multi-modal commuting, which is expressed as a discrete additional task to be accomplished. I perceive this speaker as saying "If it wasn't bad enough that I have to commute by train, once that commute segment is finished, I also have to take a bus" or "Even after I've taken the train, there's still a bus ride I have to take."
Thus "the train" is just referring to using a particular transit network, but "a bus" is an extra thing added on. Using the indefinite article 'a' highlights it as task to be accomplished, instead of just making use of a particular type of transit system. Think of it as making the bus the "straw that broke the camel's back".
Some answerers and commenters have mentioned that repeating either 'the' or 'a' for the pair would be disfavored for reasons of prosody--that it "just doesn't sound right" to repeat them. However, Google NGram for the combinations of these phrases does not support this assertion: "the train and the bus" and "a train and a bus" (using the same article for each) are roughly equally common with each other, and both are far more common than "the train and a bus" individually. This suggests that using "the" and then "a" must have some sort of more precise meaning; the choice wouldn't be automatic. I can't point to a rule or a study that says my reading is the correct one--and certainly others are possible!--it's just the context and psychology that seem most obvious to me, in trying to explain a phrasing choice that is not the result of any explicit rule I was ever taught.