There is no direct connection from Whittier to Juneau. However, you can take the bus to Anchorage airport, fly to Juneau, then take the line 5 bus to Juneau. Alternatively, Alaska DOT operates a car ferry from Whittier to Juneau once a week. Tickets cost $150 - $220 and the journey takes 23 h.
From Whittier Cruise Terminal - Alaska bus to Anchorage airport, fly to Juneau airport, then line 5 bus to Juneau. 5 h 13 min $302. From Whittier car ferry to Juneau, taxi to Auke Lake Way, then line 5 bus to Willoughby Avenue and Egan Drive. 47 h 56 min $194.