Yes, BITTERNUT is a Scrabble word!

Letter values in Scrabble US: B 3, I 1, T 1, T 1, E 1, R 1, N 1, U 1, T 1.

Is it a valid word?

BITTERNUT is a valid word in the official Scrabble dictionary (US) and the UK Scrabble Dictionary, but not in Words with Friends (ENABLE).

hickory of the eastern United States having a leaves with 7 or 9 leaflets and thin-shelled very bitter nuts

Also: bitternut hickory, bitter hickory, bitter pignut, swamp hickory, carya cordiformis.