How can I achieve even browning on the bottom of baked buns?
You may wish to try a dark colored baking sheet, such as this one from Chicago Metallic (not an endorsement, I haven't tried it.)



The dark finish will help absorb radiant heat, which is a major mode in baking, and better brown the bottoms.  In fact, such a tray probably would bake too fast for the bottoms of cookies.

Buttering it will also help conduct heat from the pan to the bottom crust, although you will also get a touch of that almost-fried texture (I like it, but it might not be what you have in mind).