The initiative bonus is assigned as a token to one unit. If that unit happens to be the Bolla, then yes. If you have another unit with MHQ, then that'd be a good situation to not give it to the Bolla at the start of the game.
Note: the initiative tokens aren't actually related to BI. It doesn't matter whether you have more BI points than your opponent, it just matters that you fit the criteria for each possible token.