Often, I will email each contact after an event with a “good to meet you” sort of message. If they have potential as a client, then yes, there is an offer to pique their interest. Beyond that point, I’d like to know if you keep up the contact? For how long, how often, and what do you do by way of personal contact to keep visible? Do you track your contacts, and if so, how?
It is hard to tell from your question what the actual situation is. Are these potential new clients for you that you got their business card from at the expo or networking event? If so, I’d call each of them and offer a special new client or first time rate or offer. Usually referrals come from existing clients that you may get referrals from – but do not hesitate to ask for referrals from your existing clients. You can set up a referral program where you give the referring client a free session or sessions for each referral. You might need to stipulate that the new referral needs to sign up for a package or some minimum number of sessions. Hope this helps.