How long does it take to mull something over?

Mulling takes an indeterminate time. If you're mulling wine, you heat gently, and add spices; it might take twenty minutes. If you're mulling over a life-changing decision, you might take several weeks, possibly longer. Anywhere in between might be counted as mulling.

I don't believe that the word mulling in your context has any period of time associated with it. It refers to the act of thinking something over or considering something in one's own mind or as a group. Your audience may have assumed a week for a response simply because they estimated it would take that long. If their question was indeed important you may have been better off giving them an explicit timing for your response: "...we'll mull it over and give you an answer tomorrow."

Mulling something over is vague time-wise; you can safely assume a week, and probably longer.

The phrase is troublesome not just because it is vague, but also doesn't convey a sense of serious consideration; it sounds half-hearted. It's best to avoid it in a business e-mail.