Differentiating between BubbleSort and InsertionSort
Unfortunately, your problem statement is contradictory, so the problem cannot be solved in its current form.  Your question states that we can obtain the running time for finite values of $n$.  However, it also states that we only learn the asymptotic running time.  This is self-contradictory, because it is not possible to infer the asymptotic running time based on any finite number of measurements.

If I had to speculate, I'd guess that maybe what the instructor actually wants you to do is find an infinite sequence of inputs $a_1,a_2,a_3,\dots$ such that: (1) $a_i$ is an array of length $i$; (2) the asymptotic running time of Insertion Sort on these inputs differs by more than a constant factor from the asymptotic running time of Bubble Sort on these inputs.  If that's correct, your next step should be to investigate various ways you might construct such a sequence.  I emphasize that this is only speculation, and not something that can be definitively derived from the problem statement as provided.