It depends. Do you need an enhanced DBS, or a standard one? If it's only a standard one, you can get one done on yourself by going through the Scottish system (also possible in England). If you need an enhanced one, you need to go via an umbrella body.
You need to find an umbrella body who will apply on your behalf, you cannot apply for one for yourself, if it's an enhanced one that you need.
What area do you work in? I work as a private tutor, and was only able to get a DBS when I did some tuition through a school who applied and paid for me. Can you get any work, voluntary or otherwise, through an organisation that will apply for one for you?