What makes a bee a mammal?

No. Individual bees are insects in the order Hymenoptera.

The superorganism of a bee nest shares many of the characteristics of a mammal:

Mammals produce few offspring: just like the bee nest.

Mammals produce milk for their young: Bees produce milk (royal Jelly) for their young.

Mammals have a uterus that allows their young to develop away from the external factors such as weather and temperature. Bee nests have a social uterus to maintain a controlled and protective environment for their young.

Mammals have a body temperature of approximately 36 degrees: A bee nest maintains a temperature of around 35 degrees.

Mammals have the ability to learn: Bee nests have the ability to learn and adapt to their environment.

(For a more detailed analysis of bees as an superorganism read 'The Buzz about Bees' by Jurgan Tautz available from many internet retailers.)