The person said they are an introvert meaning they are shy and terrified. Networking events or any other event won't fix the problem. being an introvert can actually be a positive.  My doctor is a complete introvert where I and a sales person.  I choose him specifically for that reason. I don't want my doctor rambling on about whatever. I want him to focus on me and get down to the bottom of why I am there.   Introverts are usually more analytical and in my opinion can be a huge advantage. The bottom line is anyone who says they are not nervous or terrified when speaking to someone for the first call is lying.  I was extremely terrified until I learned not to be and that only comes with practice. The more you do it the more second nature it will come. You will always have those butterflies just not as bad, we all do. Find a coach yourself or  ask to shadow the most sucessful person in your field. 
What is your real fear? Is it rejection? If you are selling your service and you are afraid to speak to the person it is automatically a no. If you do speak with them you at least have a 50% chance of a yes.