As far as I can tell, ASIO has no function to control the device volume.
The ASIO settings in Media Center has a "Volume Device" section, and System Volume control works correctly via ASIO when playing PCM.
I do have to select the correct device manually with my DAC though. 'Automatic' seemed to adjust the volume level of the default system device. (which is not always my DAC)
There are two issues here really:
One is an ASIO-specific problem, and the other is a bitstreaming problem.
The first issue is that ASIO lacks the "maximize device volume during playback option" that WASAPI has.
If my DAC is set to 80% volume in Windows, bitstreaming breaks because my DAC's ASIO driver, like many DACs, does not bypass the system volume level.
If Media Center had an option to set the device volume to 100% automatically when playback starts, like it does with WASAPI, it would fix bitstreaming via ASIO.
The second issue is more of a general usability issue, which is that bitstreaming should
always set the device volume to 100% whether that option is selected or not.
There are reasons why someone may not always want playback to maximize the device volume, but bitstreaming requires it.