A "bit of a dick" is literally a subsection of a
penis, as for example the foreskin might be. Especially after it is detached from the main.
However the meaning is metaphorical, and is distinct from being an "utter dick" a "complete dick" and variations of the same.
"Being a dick" (utter, complete, etc) is to have a
tiny thread of
logic to your words or actions, while completely missing the point, being socially autistic, probably causing offence and
maybe causing physical harm to an innocent.
Being a "bit of a dick" is therefore to meet the above criteria, but to be too personally insignificant to really cause more than a flicker of annoyance or a moment of disdain. Something like being
head-butted by an angry chicken.
Everyone agreed the traffic
warden was being a bit of a dick for ticketing the
ambulance as the paramedics
gave first aid by the roadside.