To connect our company's LinkedIn profile, do we have to first connect with a personal LinkedIn profile?

In order to connect a LinkedIn company profile (which is not a user profile), you'll need to do that by going to your SocialBee dashboard, scrolling to the bottom, and choose the LinkedIn Company button. 

However, as it's the case for Facebook pages or groups, you will need to connect by using a LinkedIn user that is an Administrator of the LinkedIn Company that you want to connect.