Since the group already had a direction of where to go for their next plan, they no longer waste any more of their time.
On that same day, they decided to make their way back at Magus Academia so that they can start working with their plan as soon as possible.
Obviously, they have no other means of transportation aside from their spiritual beast. This is the best choice that they got so far. If they wanted to arrive earlier in their school.
Instead of using the typical transportation such as the ship that they use to sail their way to Magus Academia. It is better for them if they will going to use their own beasts.
Using an analogy in Mu Lingxi's previous life, it is like the difference between commuting using public transportation against commuting using your personal car. The latter is far more convenient.
