I have suddenly developed numbness on the bottom of my tongue and on the soft tissue directly under it in my mouth. is this something neurological?

Possibly: This area is innervated by a branch of the lingual nerve which also delivers sensation from that side of the tongue. If the top surface of the tongue isn't involved then the entire nerve isn't involved. I think i would watch it for a couple weeks but see md if the numbness progresses or fails to improve.

See a dentist: There is a neurologic component to this, but i would recommend you see a dentist first to rule out any tooth/gingival infection. If everything seems normal, i.e. No infection, then i would recommend seeing an oral surgeon for evaluation.