I don't really have an email list or the patience to build one, can I buy one instead and publicize my business?
No, no, no, and no! The reason is simple: TRUST! The people on the email list that you are buying didn't choose to receive anything from you. Probably your emails will end up in the spam folder, or even if some of them open those emails would be pure luck if even one of them converted into a client. Do the right thing here.