In template memberlist FIND:
<if condition="$vboptions['usepopups'] AND !$show['usergroup']">
REPLACE that with
<if condition="$vboptions['usepopups'] AND !$show['usergroup'] AND (is_member_of($bbuserinfo, 10) or is_member_of($bbuserinfo, 11))">
Still in the same template FIND
<td class="vbmenu_control" id="memberlist_search"><a href="memberlist.php?$session[sessionurl]do=search">$vbphrase[search_members]</a> <script type="text/javascript"> vbmenu_register("memberlist_search"); </script></td>
REPLACE that with
<if condition="is_member_of($bbuserinfo, 10) or is_member_of($bbuserinfo, 11)">
<td class="vbmenu_control" id="memberlist_search"><a href="memberlist.php?$session[sessionurl]do=search">$vbphrase[search_members]</a> <script type="text/javascript"> vbmenu_register("memberlist_search"); </script></td>
</if>
10 and 11 are examples for the IDs of usergroups you want to grant access,
Use as many OR clauses ys you've got usergroups which should have access.
However, this will NOT stop them from searching the memberlist - it will just remove the links & form.
If you want to reliable prevent unspecified usergroups from searching the memberlist you will have to create a new usergroup setting "Can search memberlist [yes/no]" and check for this permission in memberlist.php