Or you can apply HighlightBrushKey directly to the ListBox. Setter Property="Background" Value="Transparent" did NOT work. But I did have to set the Foreground to Black.
<ListBox ... >
<ListBox.ItemContainerStyle>
<Style TargetType="ListBoxItem">
<Style.Triggers>
<Trigger Property="IsSelected" Value="True" >
<Setter Property="FontWeight" Value="Bold" />
<Setter Property="Background" Value="Transparent" />
<Setter Property="Foreground" Value="Black" />
</Trigger>
</Style.Triggers>
<Style.Resources>
<SolidColorBrush x:Key="{x:Static SystemColors.HighlightBrushKey}" Color="Transparent"/>
</Style.Resources>
</Style>
</ListBox.ItemContainerStyle>
</ListBox>