I have an Android phone, so I use the Google Voice app to send text msgs to make sure my real number doesn't come through. Make sure to text through the GV app and set the phone to ask if you wish to make calls using GV or not. It's pretty easy.
Back to the OP's question, it's all about risk in my opinion. I'll explain.
I'm single and only see well established ladies. I don't take risks with seeing anybody that doesn't have a good history. Being single, I don't have anybody to worry about looking through my phone. As a result, I feel it's worth the risk of using GV for the convenience.
However.... if I had a SO, or if I were taking more risks in regards to who I was seeing, jframe2 is dead on about all the precautions to take. A burner phone is definitely the way to go.
Funny thing when I started trying to get into the hobby. I got a burner phone and left it on a side table at home. A buddy dropped by to drink a few and hang out one night. He saw the phone and started asking why I would need a burner phone and asked if I was okay. LOL