If you work from home, you may need a business owner's policy. This is often not a set rule. Rather, it is a look at your overall insurance needs.
Is There A Rule That You Need BOP Insurance?
There is rarely going to be a rule that you need BOP insurance. The only types of insurance that are broadly required by law are auto insurance and workers compensation insurance. Some professions also have regulations that require them to carry additional insurance. 
If you need to get permission to work from home from your homeowners' association, condo association, or apartment community, they might require you to have a certain amount of insurance to protect the community. This would usually be general liability insurance that you can get as part of your business owner's policy.
Does Working From Reduce Your Insurance Needs?
Working from home doesn't usually change your insurance needs. The major way it would change your needs is if you never have clients come to your home and don't need to worry about them getting hurt when they visit you. However, you'd still likely need general liability insurance to cover you in the event you accidentally injure someone or damage their property while you're out meeting clients.
You also shouldn't make the mistake of assuming your home insurance will cover you since you're at home. The liability portion of your policy will virtually always exclude any type of business activity. Your property coverage may provide limited protection for your business equipment, but it usually won't be enough if you have anything of substantial value.
Finally, if you do any type of work that could lead to someone getting hurt or a client losing money, you still need insurance to protect against those risks.
What Does BOP Insurance Cover?
A business owner's policy is a package deal of different types of common business insurance coverages. It usually includes general liability and commercial property protection, as well as coverages tailored to your specific business activity. For example, the insurance company might sell one package to plumbers, another to lawyers, and another to computer programmers. Each package has different prices based on several factors, including how much time you spend in an office versus doing dangerous work. So, you can easily find affordable coverage for a home-based business.