The experiment performed in the OP could let one determine that wood does not matter. But, it cannot let one determine that wood does matter (meaning, the species of wood).
Long version:
If you think all the recordings in the sound the same, then you can conclude that (at least, to you) the species of wood does not matter (when comparing ash to alder).
But, if you think the recordings sound different, and can identify which 2 where Bass Body 1 and which 2 were Bass Body 2, then you cannot conclude that the difference is because of the species of wood.
It could be that 2 different alder bodies would also sound different to you. Or 2 different ash bodies.
As we all know, there are lots of basses made from the same species of wood that are quite different in weight. Compare an early 60s ash Fender to an "identical" late 70s ash Fender. Similarly, compare different EBMM StingRays.
I think we all also know that many different basses that are the same model and wood sound different to each other.
So, getting back to the point, if you can tell a difference between the sound of these two bass bodies (in the OP), how do you know it's because of the different species of wood? You might just as easily hear the same difference between two ash bodies or two alder bodies.
Long version:
If you think all the recordings in the sound the same, then you can conclude that (at least, to you) the species of wood does not matter (when comparing ash to alder).
But, if you think the recordings sound different, and can identify which 2 where Bass Body 1 and which 2 were Bass Body 2, then you cannot conclude that the difference is because of the species of wood.
It could be that 2 different alder bodies would also sound different to you. Or 2 different ash bodies.
As we all know, there are lots of basses made from the same species of wood that are quite different in weight. Compare an early 60s ash Fender to an "identical" late 70s ash Fender. Similarly, compare different EBMM StingRays.
I think we all also know that many different basses that are the same model and wood sound different to each other.
So, getting back to the point, if you can tell a difference between the sound of these two bass bodies (in the OP), how do you know it's because of the different species of wood? You might just as easily hear the same difference between two ash bodies or two alder bodies.