Well i would slave the drum machine to the ASR or just trigger the notes via the ASR since the ASR has a 16 track sequencer where the boss has 4.
Anyway, One has to be set to slave mode and the masters midi out has to be connected to the midi in of the other device. Look in your manuals and find out how each behaves as a slave since there are probably some limitations like only playing in song mode when slaved.
When set up right, hitting start on one will start the other