How can a single owner buy disability insurance for themselves?

Depends on what you are trying to secure and industry in working

A variety of insurance companies offer coverage for long-term disability for business owners and other high earners. These policies have longer elimination periods, and pay benefits until age 65 in many cases. Contact an insurance agent who specializes in disability insurance.

The coverage of short-term disability is more difficult to find.  

These policies have short elimination periods, and payment of benefits up to 2 years. If you want to cover accidents and diseases are only a few companies that offer policies to people.

If you are looking 

To cover pregnancy, short-term plans only disability in the market are sold as voluntary employee benefits. If you work as a contractor in 1099, that entity may allow you to purchase coverage through payroll deductions.