TicketStumbler is my third business and the closest thing I've ever done to a business plan is the YC application form. Know what problem you're solving, why you're solving it, who has this problem, how you're going to solve it and (maybe) monetization options.

I think a business plan could be important if you're looking to take gobs of money, but your query makes it sound like the investors are angels. Maybe providing more details would help everyone provide further feedback?