How do I protect my idea before I hand it over to an attorney for a patent search?

There is no need to fear your attorney. Attorneys would not keep their licenses very long if they stole inventions from clients. All attorneys are bound by state ethics rules that require confidentiality. For example, Washington State lawyer are obliged to follow RPC 1.6 which states that A lawyer shall not reveal information relating to the representation of a client unless the client gives informed consent, the disclosure is impliedly authorized in order to carry out the representation or the disclosure is permitted in certain limited circumstances such as to prevent reasonably certain death or substantial bodily harm, to prevent the client from committing a crime, etc.