Edit your postbit (and postbit_legacy) templates...
Put the entire code inside this conditional:
Code:
<if condition="!$show[guest]">
*all original code here*
</if>
That will show nothing to anyone who is a guest.
If you want to show something in place of nothing try:
Code:
<if condition="!$show[guest]">
*all original code here*
<else />
Guests cannot see this data.
</if>
That said, you should probably just use forum permissions to make guests not be able to view any threads rather than doing this template edit.