When and to where can I take a person with me using my VGM semester ticket?

That's what it says http://muensterland-tarif.de/tickets/zeittickets.html under "Semesterticket" – "Münsterland":

Until and including summer semester 2016, the participation of other persons is excluded.

Additional from winter semester 2016/17:

Holders of a semester ticket Münsterland are allowed to take a child from 6 to 14 years of age without time restrictions.

In addition, the bus ride in the cities of Münster, Bocholt, Rheine and Hamm is extended by another person or bicycle. This scheme applies on working days from 7 pm and on Sundays, Saturdays and holidays without time restrictions.