Even I'm a bit of a bookworm, you know.

Literal

I [too-だって] a-bit reading-person is [explanatory-んだよ].

ちょっとした is a fixed expression meaning 'a little, a bit of a, somewhat' — used to soften a claim of being something. 読書家 ('reader, bookworm') combines 読書 ('reading') + 家 ('person, expert'). A self-deprecating boast — 'I'm something of a reader.'