In a large bowl, combine whipping cream and sugar. Whip until stiff peaks. In another bowl, whip mascarpone, bananas and salt until fluffy, about 1 minutes. Gently fold whipped cream into mascarpone mixture just until combined.
In bowl, combine espresso, rum and sugar; mix to dissolve. Dip each ladyfinger quickly into espresso mixture (do not let them sit in it) and place into a single layer in a 9x13 inch dish. Top with half of cream mixture. Repeat with remaining ladyfingers and cream mixture. Top with sliced bananas, shaved white chocolate and cocoa powder. Cover and refrigerate for 4 hours or overnight.