This is a tough question to answer. Conversationally, or colloquially, I think that any English speaker would know what you meant with this sentence.
However, if my knowledge of "proper" grammar isn't failing me, then there is one thing you would have to change about this sentence to make it 100% technically correct.
"He asked what I would do tomorrow if I *weren't* busy at my office."
The use of "would" makes the tense of that whole phrase conditional. We typically use "were" or "weren't" in a conditional tense.
Example: I wouldn't touch that rattlesnake if I were you!
Hope that helps!