1) a Bolshevik, or someone accused of having Bolshevik (
communist) leanings).
2) (more commonly) an adjective meaning that someone is very assertive in the pursuit of
something and/or hostile to authoritarian manoeuvres by others. A bolshy
person gets cross if confronted and is likely to say "what's it to you?", "mind your own business" and stuff like that a lot.
3) also the name of a short-lived youth magazine run by the Alliance for Workers' Liberty.