Thanks for pointing that out, I never realised there were references to levels in the anime.
It's not going to change the concepts for this game though, as even if there are levels in the anime then they're not visible anyways.
According to this screenshot, I've left my Bulbasaur and Metapod training in different dojos. (Different dojos = different stat bonuses). Looks like its going to take a while before Bulbasaur completes his Speed Training though, .
[The stronger the Pokemon in whichever stat you're training it, the longer it takes to complete it's workout)