The only bus to Kuala Perlis is from Kangar, via the Cityliner bus station in the centre of town. Buses leave daily from 08:45 to 19:30 nearly every hour and take 20 minutes, excepting Fridays when they there is a longer gap around noon for prayers. The bus will either take you straight to the Langkawi jetty terminal or drop you off at the intersection before doing a turn back to Kangar.
Taking a taxi from Kangar to Kuala Perlis takes about 15 minutes and the set rate is 14 ringgit -- it's the same heading out of Kuala Perlis as well. From Kuala Perlis taxis leave from the jetty terminal building, upon getting enough customers. The rate for Alor Setar is 40 ringgit and to Arau train station 28 ringgit.