Yes, BUSIEST is a Scrabble word!

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

Is it a valid word?

BUSIEST is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

actively or fully engaged or occupied
overcrowded or cluttered with detail
intrusive in a meddling or offensive manner
crowded with or characterized by much activity
(of facilities such as telephones or lavatories) unavailable for use by anyone else or indicating unavailability; (`engaged' is a British term for a busy telephone line)

Also: in use.

Not playable in Scrabble US: BUSYBODIED.