"Die Maus spielt mit einem Bären"
"Die Maus spielt mit einem Bären" == "The mouse plays with a bear"?
"Bären" is the plural form of "Bär" (bear) and "einem" (one) indicates singularity of the object. So this phrase is saying "one bears", and it is conflicting (confusing), at least in English.
Is this a special rule (in a lesson that I have missed) in German? E.g. it must be in plural form after "mit"?
I am not a specialist, but I think it is no mistake.There is actually a category of masculine nouns whose endings change according to the case. Bär is one of them. They are called masculine weak nouns. Maybe this link will be useful: http://www.vistawide.com/german/grammar/german_nouns03.htm