Scoop the ice cream into a food processor. With the machine on, add the bourbon and process just until blended. Pour the ice cream into a large, shallow plastic container, cover and freeze until firm enough to scoop, about 30 minutes.
Whip the cream with the vermouth, sugar and bitters until firm. Refrigerate until chilled.
To serve, fill 4 pint glasses two-thirds full with cherry soda. Divide the ice cream between them and top each glass with a dollop of the whipped cream. Garnish each drink with 3 cherries.