。
I'm the type to adapt quickly.
Literal
Quick-change [subject-が] fast type is.
変わり身 means 'quick change' or 'adaptability' — originally a martial arts term for switching stances, now used figuratively for someone who changes positions or adapts easily. 方 (かた) here means 'type/kind of person.' The んです at the end is explanatory, providing background information.