What do you think about me asking my boyfriend's boss if he can have a day off?
Do you think your BF's boss will get angry?
I just want to spend time with my BF, and I think his boss is less likely to be angry.
I see that you just want to have time with your boyfriend, but it's not your place to talk to his boss for him. Your boyfriend will probably be mad if you do. You should talk to your boyfriend, and ask him to request a day off.
Do you know what will happen if I can't go out with my BF?
It's inappropriate to try to interfere with your boyfriend's work schedule. Discuss the matter with him and he will handle it in an appropriate manner.