TIL, this was my first time seeing the term. I just assumed that the poster had left out the second word of "bush league". That would mean something similar but subtly different, though (a lawyer not up to professional standards).
I'd imagine both terms are derogatory, no? "Bush" is usually a derogitroy descriptor of aboriginal peoples as "primitive" or "unsophisticated"
The subtle difference is not that one is neutral. It's that "bush league lawyer" is a bad lawyer, but "bush lawyer" can be either that or someone attempting to act as a lawyer without actually being one.
I've heard a similar formulation of "barracks lawyer" from military folks. The dude who gives terrible advice but can use enough legal jargon to make it sound convincing.