6 stat boosts is the highest you can have. For example, you can only use Harden 6 times before you can't use it anymore. If you were able to get more than 7 boosts, you would eventually be undefeatable. That's how Game Freak probably wanted it to be.
The reason why you used Bulk Up 7 times and it still worked is because your stats got lowered while you were using Bulk Up and you didn't realize it.