how to grant permission for a group of people to join when 1 person pays for access..

[Princeton]

I would just create a usergroup for each paying client, and add the members of that company to the right group. If the subscription is finished, you remove the usergroup.

Yep, this is the easiest way of doing it with a default vBulletin; but, it is the most expensive way. (eg. time is money and upgrading each member that joins will take up a lot of time)

I recommend creating a custom "access code" script.
Whenever access code is used, the member will be promoted to the new usergroup.

• You make the options available for members to purchase access to forums for their employees.
• The members will have to choose between 10, 25, 50, 100, etc employees. (I would charge a different amount for each group.)
• Upon a purchase, the system will automatically send buyer a "THANK YOU" email with the access code and instructions.
  • The instructions will instruct the member to give out this access code to all his employees.
  • The instructions will instruct buyer to approve all members who use access code. eg. Tom uses the access code to upgrade membership ... Bob, the buyer/boss, will have to approve the upgrade/access

Yea, it's a bit complicated but it will make life easier for you.
The system should be made so that sharing of access code will be limited to only the employees. Hence, the buyer has to approve each upgrade.