Place white chocolate in a heatproof bowl set over a pan of simmering water, stirring occasionally, until chocolate melts. Remove from heat.
Melt bittersweet chocolate in a heatproof bowl set over a pot of simmering water, stirring occasionally. Stir in peanuts. Spread on a parchment-lined rimmed baking sheet, spreading peanuts in a single layer. Drop spoonfuls of white chocolate on top, and swirl chocolates with a skewer. Refrigerate until set, about 1 hour. Break bark into large pieces. Bark will keep, covered and refrigerated, for up to 2 weeks.