Place the freeze-dried raspberries into a food processor and blend until a fine powder forms.
Set a fine-mesh sieve over a small bowl. Sift the raspberry powder to remove seeds or larger bits. (You should have about ⅓ cup of powder from 1 ½ cups of freeze-dried raspberries.) Set the powder aside, reserving about 2 teaspoons for garnish.
Place the chopped white chocolate and butter into a large heatproof bowl.
In a small saucepan, add the heavy cream. Heat over low heat until it just begins to simmer, do not let it boil.
Pour the hot cream over the white chocolate and butter. Let it sit for 5 minutes without stirring.
Gently stir the mixture until smooth and fully combined and melted.
Add the raspberry powder, one tablespoon at a time, whisking well after each addition.
Cover the bowl tightly with plastic wrap and refrigerate for 2 hours, or until the mixture is firm enough to scoop.
Line a baking sheet with parchment paper.
Using a 1-tablespoon scoop, portion out the mixture into balls (makes about 26 truffles), placing each on the lined baking sheet.
Chill the balls in the refrigerator for 30-45 minutes, or until firm.
When ready, place the chopped bittersweet chocolate into a large heatproof bowl. Melt the chocolate using a double boiler (set the bowl over a saucepan with an inch of simmering water, making sure no water touches the chocolate) or in the microwave in 20-second bursts, stirring between each until smooth.
Remove the truffles from the refrigerator in small batches to prevent them from getting too soft. Working one at a time, gently drop each truffle into the melted chocolate, making sure it is completely covered.
Using a fork, lift out the chocolate-covered truffles. Use a toothpick or another fork to slide the truffle onto the parchment-lined baking sheet.
While the coating is still wet, sprinkle a little reserved raspberry powder over the top for garnish, if desired.
Let the truffles set at room temperature for about 1 hour, or refrigerate for 15 minutes to speed up setting.
Store in an airtight container in the refrigerator for up to 1 week, or freeze for longer storage.