The Bay Street Theater in Sag Harbor will be a busy venue this week, with four days of films, music, and dancing, starting today at 6 p.m. with a screening of “The Winter Guest,” a drama directed by Alan Rickman about a widow determined to leave Scotland who gets an unexpected visit from her aging mother. Starring Phyllida Law and Emma Thompson, it was shown in 1997 at the Hamptons International Film Festival. Tickets are $10.