They are all fine. If one of them comes much more easily and naturally to you, use it. In your first example, "I can take the bus" is plain, "I can catch the bus" has a very slight "twist" to it. In your second example, "I can pick up my daughter at the airport" is plain, "I can fetch my daughter from the airport has a very slight "twist" to it. By "twist" I mean a tiny overlay that changes the tone very slightly. It could either be a subtle shade of meaning, or someone trying to add just a little bit of personality or variety to their speech. To "catch" the bus emphasizes the bus schedule and the possibility that you might get there slightly too late and "miss" the bus. Thus, my daughter-in-law might say "Can you get to our house by 12:30?" and I might say "Yes, that works well, I can catch the 11:17 train." If she said "There's a huge traffic jam in the roads, is there another way to get here?" I might say "Yes, I can take the train." But I could also say "I can catch the train" as a kind of little cheerful twist, just as I might say "I'll hop on the train" or "I'll grab the train." In U.S. English, "fetch" carries the idea of something that's a slightly unpleasant duty or chore, possibly something you've been ordered to do. A typical context might be "My wife has a list of things for me to do today: buy the Christmas tree, wrap the presents, and fetch my daughter from the airport." In other words, my daughter would probably not want to hear that I was "fetching" her from the airport because it suggests that I'm doing it dutifully rather than cheerfully.

In your examples, they are used interchangeably and both sets sound fine. Examples I take the bus to Minnesota or you can say ride thge bus to Minnesota. I catch the ball. The dog will fetch the ball Jack and jill went to fetch a pail of water (get).