Place the cream in a heat-proof bowl and set the bowl over a pan of simmering water. Cook until heated through.
Using a wire whisk, slowly stir the white chocolate into the warm cream until completely melted. Whisk in the Baileys and vanilla.
Cover and chill for one hour or until pliable but firm enough to scoop.
With two teaspoons or a 1 1/4-inch ice cream scoop, make dollops of the chocolate mixture and place on a baking sheet lined with parchment paper.
Refrigerate for about 15 minutes, until firm enough to roll into rough spheres.
Melt the bittersweet chocolate in a heat-proof bowl set over a pot of simmering water.
Drizzle the melted bittersweet chocolate over the truffles. Chill until ready to serve.