I have written business plans for all manner of industries: a coin operated jukebox company, airlines, travel companies, new product launches, and anti_aging product companies. It is not necessary to have a passion for the product or the company to write or develop a business plan. What you must have is a passion for aggregating information, getting involved with and understanding the service or product, and understanding the financials of the product or service. By financials I am not referring to having a CPA before you undertake the task, but rather understanding the presentation of the information and analysis/ numbers to support the activity being planned. Financials are important because they are the score card in the world of commerce.
For an online business, a detailed and in depth business plan is usually not necessary unless you are trying to combine your online business with a traditional business. For most online business startups, the detail involved with planning a traditional business is not required. However, it would still be beneficial to you if most of the topics were still covered, even if only briefly. Having a written plan in front of you will help you to focus on important aspects of the business.