there are different ways to make this happen, if you always wanted to wait one measure, you can set the Aeros to count in for one bar in the song settings.
If this is not perfect for your set up, you can also set the Aeros to only playback when it receives the midi start command. The BB sends this at the start of the first part. You can set this in the Aeros device settings in the Main Menu.
What will happen is the Aeros will enter a scrolling mode, where it is following the BeatBuddy, but it will not start recording until you set up a recording.